1
The angle while looking at the top of a tower is —
💡 Hint:
The head is up.
Explanation:
An angle of elevation.
Class 10 · Maths · Chapter 9 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Some Applications of Trigonometry
Some Applications of Trigonometry
How to use this page:
1. Read — Line of sight · elevation · a rope as hypotenuse · broken tree · two angles · depression, diagram, worked example, board tip
2. Check — each lesson has its own questions; the number follows the lesson
3. Mastery ★ — all of that lesson correct. Redo the wrong ones
4. The memory figure shows a tower, the horizontal ground and the angle of elevation, and writes tan = height/distance.
Progress stays in this browser.
🏅 Your achievements — 0/6 badges
🔥 0day streak · longest 0
⭐ 0total XP · today 0
🎓 1level
Next level: 150 XP to goright answer +10 · after a hint +5 · review +6 · badge +25
Last 7 days:
Everything is saved in this phone/browser — no login.
- 1 Line of sight, elevation and depression
- 2 Height from one angle of elevation
- 3 Rope, slide and string
- 4 A broken tree
- 5 Two angles of elevation
- 6 Distance from an angle of depression
- Chapter winner — every lesson at mastery ★
🎬 Shorts
This chapter has no Short on the channel yet, so ten empty cards are not shown. The notes, diagrams and checks are complete.
📄 PDF download — notes + answer key
Line of sight, elevation and depression
दृष्टि रेखा, उन्नयन और अवनमन · NCERT 9.1 · the names, then the exercise
Above or below the horizontalNotes
The line from the eye to the object is the line of sight. The angle above the horizontal is elevation. The angle below the horizontal is depression.
Looking at the top of a tower, the head rises: that is elevation. Looking down from a balcony at a flower pot, the head lowers: that is depression. These two names are fixed before exercise 9.1. The angle is made with the horizontal, not with the wall of the tower.
Write the direction of the head firstActivity
If the eye is on the ground and the line goes up, it is elevation. If the eye is up and the line goes down, it is depression. One line of sight does not take both names. Do not use tan before the name is written.
Worked exampleExample
Question: One student looks at the top of a tower. Another looks from a roof at a person on the road. Name the angles.
Formula: A sight upward is elevation, a sight downward is depression.
Substitution: The first sight is above the horizontal. The second is below the horizontal.
Answer: The first is an angle of elevation. The second is an angle of depression.
10-second revision
- Elevation = above the horizontal
- Depression = below the horizontal
- The angle is not made with the wall
Board tip · BSEBBoard tip
In a BSEB answer write the word “elevation” or “depression” first, then the figure.
Board tip · CBSEBoard tip
On CBSE do not call both the same angle. The direction of the head is different.
Check your understandingall correct = mastery ★
2
The angle of depression is formed below the horizontal.
Explanation:
True — the head lowers.
3
The line from the eye to the object is called the ______.
💡 Hint:
The line of looking.
Explanation:
The line of sight.
4
Looking from a roof down to the road is —
💡 Hint:
The line goes down.
Explanation:
Depression.
5
Write one difference between elevation and depression.
Model answer (board format)
Elevation is above the horizontal and depression is below the horizontal. Both are angles of the line of sight.
Check your answer:
Height from one angle of elevation
एक उन्नयन कोण से ऊँचाई · Exercise 9.1 · a tower and tan
Height = distance × tan of the angleNotes
The tower is vertical, so the right angle is at the foot. If the angle on the ground is C and the distance is BC, then tan C = AB/BC, so height = distance × tan C.
At 45°, tan = 1 and the height equals the distance. At 30°, height = distance/√3. At 60°, height = distance × √3. The tower question in exercise 9.1 is this. Keep the unit metre. Leave √3 in the answer unless the question asks for a decimal.
Put the right angle at the footActivity
If the distance is 20 m and the angle is 45°, then tan 45° = h/20. 1 = h/20. h = 20. If the distance is 30 m and the angle is 30°, then h = 30 × 1/√3 = 10√3. Without a figure the sides of the ratio get swapped.
Worked exampleExample
Question: From a point on the ground 20 m from the foot of a tower, the angle of elevation is 45°. Find the height.
Formula: tan 45° = height / distance.
Substitution: 1 = h / 20.
Answer: h = 20 m. Check: at 45° the opposite and adjacent sides are equal.
10-second revision
- tan = height/distance
- At 45°, height = distance
- The unit is m
Board tip · BSEBBoard tip
In a BSEB answer write the tan line, then the substitution, then the metre.
Board tip · CBSEBoard tip
On CBSE write 10√3 m at 30°. Write 17.3 only when the question says so.
Check your understandingall correct = mastery ★
1
If the distance is 20 m and the elevation is 45°, the height of the tower is —
💡 Hint:
tan 45° = 1.
Explanation:
20 m.
2
If the distance is 30 m and the elevation is 30°, the height is 30 m.
Explanation:
False — the height is 30/√3 = 10√3 m.
3
If the distance is 30 m and the angle is 30°, the height is ______ m.
💡 Hint:
30 × 1/√3.
Explanation:
10√3 m.
4
If the distance is 10 m and the elevation is 60°, the height is —
💡 Hint:
tan 60° = √3.
Explanation:
10√3 m.
5
The angle of elevation sits at the ground corner when the eye is on the ground.
Explanation:
True — the opposite side is the tower.
6
The elevation is 45° from a point 15 m from the foot. Find the height.
Model answer (board format)
tan 45° = h/15. 1 = h/15. h = 15 m.
Check your answer:
Rope, slide and string
रस्सी, फिसलपट्टी और धागा · Exercise 9.1 · questions 1, 3, 5 · hypotenuse
The slanted length is the hypotenuseNotes
A rope, a slide or a kite string makes an angle with the ground. Height = length × sin of the angle. Length = height / sin of the angle.
sin 30° = 1/2 and sin 60° = √3/2. The string is taken with no slack, which is the condition in the exercise. cos is used when the distance along the ground is needed: distance = length × cos of the angle.
Decide which side is the one givenActivity
A 10 m rope at 30°. The rope is the hypotenuse. Height = 10 × 1/2 = 5 m. If a slide is 3 m high at 60°, the length = 3 / (√3/2) = 2√3 m. Do not treat the height as the hypotenuse.
Worked exampleExample
Question: A 10 m rope makes 30° with the ground. Find the height of the pole.
Formula: sin 30° = height / rope.
Substitution: 1/2 = h / 10.
Answer: h = 5 m. The distance along the ground = 10 × cos 30° = 5√3 m.
10-second revision
- The rope is the hypotenuse
- Height = length × sin of the angle
- A slack string does not fit this ratio
Board tip · BSEBBoard tip
In a BSEB answer write one line of words: “hypotenuse = rope”.
Board tip · CBSEBoard tip
On CBSE do not swap sin and tan in the same question. Look at the side that is given.
Check your understandingall correct = mastery ★
1
A 10 m rope at 30°. The height of the pole is —
💡 Hint:
10 × 1/2.
Explanation:
5 m.
2
A slide 3 m high at 60° is 3 m long.
Explanation:
False — the length is 3/(√3/2) = 2√3 m.
3
For a 10 m rope at 30°, the ground distance is ______ m.
💡 Hint:
10 × √3/2.
Explanation:
5√3 m.
4
A kite is 20 m high and the string makes 30° with the ground. There is no slack. Find the length of the string.
Model answer (board format)
sin 30° = 20/L. 1/2 = 20/L. L = 40 m.
Check your answer:
A broken tree
टूटा हुआ पेड़ · Exercise 9.1 · question 2 · stump + hypotenuse
The height is the sum of two piecesNotes
The tree breaks and bends until the tip touches the ground. The stump is the vertical side. The broken part is the hypotenuse. The full height = distance × tan of the angle + distance / cos of the angle.
At 30° with a distance of 6 m, the stump = 6/√3 = 2√3 m and the broken part = 6/(√3/2) = 4√3 m. The sum is 6√3 m. Writing only the stump is half an answer. Question 2 of exercise 9.1 has this shape.
Right angle at the foot, the given angle at the touch pointActivity
Foot A, top of the stump B, touch point C. The angle is at C. AC is the distance, AB is the stump, BC is the broken part. tan C = AB/AC and cos C = AC/BC. Find both and add them.
Worked exampleExample
Question: The broken part makes 30° with the ground and the touch point is 6 m from the foot. Find the full height of the tree.
Formula: Stump = 6 tan 30°, broken part = 6 / cos 30°.
Substitution: Stump = 6 × 1/√3 = 2√3 m. Broken part = 6 / (√3/2) = 4√3 m.
Answer: Full height = 2√3 + 4√3 = 6√3 m.
10-second revision
- Stump = distance × tan of the angle
- The broken part is the hypotenuse
- The full height is the sum of both
Board tip · BSEBBoard tip
In a BSEB answer keep two lines, the stump and the broken part, then the sum.
Board tip · CBSEBoard tip
On CBSE do not stop at 2√3 m instead of 6√3 m. The sum gets missed.
Check your understandingall correct = mastery ★
1
Distance 6 m, angle 30°. The full height of the broken tree is —
💡 Hint:
2√3 + 4√3.
Explanation:
6√3 m.
2
In the same question the stump is 2√3 m.
Explanation:
True — 6 × tan 30°.
3
In the same question the broken part is ______ m long.
💡 Hint:
6 / cos 30°.
Explanation:
4√3 m.
4
In the broken tree, the hypotenuse is —
💡 Hint:
The slanted side.
Explanation:
The broken part is the hypotenuse.
5
If the distance is 3 m and the angle is 30°, find the stump and the full height.
Model answer (board format)
Stump = 3/√3 = √3 m. Broken part = 3/(√3/2) = 2√3 m. Full height = 3√3 m.
Check your answer:
Two angles of elevation
दो उन्नयन कोण · Exercise 9.1 · questions 6 to 11 · walking and two heights
The nearer angle is the larger oneNotes
Walk toward the object and the angle of elevation grows. At the first place the distance is x + d with angle 30°, and at the nearer place the distance is x with angle 60°. h = x √3 and h = (x + d)/√3.
If d = 10 m, then x + 10 = 3x, so x = 5 m and h = 5√3 m. If the eye is not on the ground, subtract the eye height from the height in the triangle. If a tower stands on a roof, write two separate tans, one for the building and one for the tower. The middle questions of exercise 9.1 are this.
Two equations, one hActivity
tan 60° = h/x gives h = x√3. tan 30° = h/(x+10) gives 1/√3 = x√3/(x+10). So x+10 = 3x. The distance walked is 10 m and the distance left is 5 m. Both angles belong to the same height.
Worked exampleExample
Question: From a point the elevation of a tower is 30°. After walking 10 m closer the angle is 60°. Find the height and the distance left.
Formula: tan 60° = h/x, tan 30° = h/(x+10).
Substitution: h = x√3. 1/√3 = x√3/(x+10). x+10 = 3x. x = 5.
Answer: The distance left is 5 m. The height is 5√3 m. The distance walked is 10 m.
10-second revision
- The angle grows as you move closer
- With 60° and 30°, the distance left is half the distance walked
- Subtract the eye height
Board tip · BSEBBoard tip
In a BSEB answer label both x and x+d on the figure. Do not run two angles from one distance.
Board tip · CBSEBoard tip
On CBSE, with an eye at 1.5 m, the triangle height of a 30 m building is 28.5 m. Do not keep the full 30 m.
Check your understandingall correct = mastery ★
1
After walking 10 m from 30° to 60°, the distance left is —
💡 Hint:
x+10 = 3x.
Explanation:
5 m. The height is 5√3 m.
2
In the same situation the height of the tower is 5√3 m.
Explanation:
True — h = 5 × √3.
3
With an eye at 1.5 m and a 30 m building, the triangle height is ______ m.
💡 Hint:
30 − 1.5.
Explanation:
28.5 m.
4
Walking toward the object, the angle of elevation —
💡 Hint:
The nearer angle is larger.
Explanation:
It increases.
5
The two angles are placed at one distance and the two tans are set equal.
Explanation:
False — the distances x and x+d are different.
6
If walking 20 m closer changes the angle from 30° to 60°, find the distance left and the height.
Model answer (board format)
x+20 = 3x, so x = 10 m. h = 10√3 m.
Check your answer:
Distance from an angle of depression
अवनमन कोण से दूरी · Exercise 9.1 · questions 12 to 15
The upper angle comes down to the ground cornerNotes
Depression is measured from the upper horizontal. The ground is parallel, so the angle at the ground corner of the triangle equals the angle of depression.
From a 12 m roof at a depression of 30°, tan 30° = 12/d and d = 12√3 m. Two boats on one side, angles 45° and 30°, cliff 40 m: the nearer distance is 40 m and the farther is 40√3 m. The gap is 40(√3 − 1) m. The last questions of exercise 9.1 are depression. If a car moves at a steady speed, time is in the ratio of the distances.
Bring the depression down to the ground cornerActivity
From a roof the angle is drawn at the top, but in the triangle used for the calculation it sits on the ground. Writing 60° between the tower and the line of sight is a miss. That corner would be 90° minus the depression. If a kite or a car has two positions, subtract the two distances.
Worked exampleExample
Question: From a 12 m roof the depression of a point is 30°. Find the distance of the point from the foot.
Formula: The angle on the ground is 30°. tan 30° = 12/d.
Substitution: 1/√3 = 12/d.
Answer: d = 12√3 m.
10-second revision
- Depression = the angle at the ground
- At 45°, distance = height
- The gap between two boats is a difference of distances
Board tip · BSEBBoard tip
In a BSEB answer write that the horizontals are parallel, so the angles are equal.
Board tip · CBSEBoard tip
On CBSE you may also write 40(√3 − 1) m as 40√3 − 40. Do not turn the minus into a plus.
Check your understandingall correct = mastery ★
1
A 12 m roof, depression 30°. The distance from the foot is —
💡 Hint:
d = 12 × √3.
Explanation:
12√3 m.
2
From a 40 m cliff, boats at 45° and 30° are 40(√3 − 1) m apart.
Explanation:
True — 40√3 − 40.
3
At a depression of 45° and a height of 40 m, the nearer distance is ______ m.
💡 Hint:
tan 45° = 1.
Explanation:
40 m.
4
A car is first at a depression of 30° and 6 seconds later at 60°. What part of the first distance is the distance left?
Model answer (board format)
With 60° and 30°, the distance left is half the distance walked, so one third of the first distance remains. Time is in the ratio of the distances. The foot is another 6 × (1/2) = 3 seconds away, because the distance already walked was twice the distance left.
Check your answer:
❓ Full question bank — with answers and explanations — 65 questions
Pick a type. The 30 lesson checks are separate — each lesson has as many as its topic needs. All correct earns mastery ★.
BSEB modelpractice · not annual60 tried · 0 correctMultiple choiceMCQ120 tried · 0 correctTrue / falseTrue / false80 tried · 0 correctFill in the blanksFill80 tried · 0 correctMatchMatch20 tried · 0 correctAssertion–reasonAssertion–reason50 tried · 0 correctBalancingBalancing40 tried · 0 correctIdentifyIdentify20 tried · 0 correctShort and longVSA, SA, LA120 tried · 0 correctCBSE-stylenot a PYQ60 tried · 0 correct
No question is marked as a verified past paper. The BSEB set is a model for practice. CBSE items are CBSE-style, not a copy of any year’s paper.
Multiple choice
0/12Pick one option. A wrong try brings a hint.
1
Looking at the top of a tower is —
💡 Hint:
Head up.
Explanation:
Elevation.
2
20 m away, elevation 45°. Height —
💡 Hint:
tan 45 = 1.
Explanation:
20 m.
3
30 m away, elevation 30°. Height —
💡 Hint:
30/√3.
Explanation:
10√3 m.
4
A 10 m rope at 30°. Height —
💡 Hint:
sin 30 = 1/2.
Explanation:
5 m.
5
A slide of height 3 m at 60° has length —
💡 Hint:
3 / sin 60.
Explanation:
2√3 m.
6
Broken tree, distance 6 m, angle 30°. Full height —
💡 Hint:
Stump plus hypotenuse.
Explanation:
6√3 m.
7
Walk 10 m from 30° to 60°. Distance left —
💡 Hint:
x+10 = 3x.
Explanation:
5 m.
8
A 12 m roof, depression 30°. Distance —
💡 Hint:
12 × √3.
Explanation:
12√3 m.
9
A 40 m cliff, a boat at 45°. Distance —
💡 Hint:
tan 45 = 1.
Explanation:
40 m.
10
Kite 20 m high, string at 30°, no slack. Length —
💡 Hint:
sin 30 = 20/L.
Explanation:
40 m.
11
Eye 1.5 m and a 30 m building. Triangle height —
💡 Hint:
Subtract.
Explanation:
28.5 m.
12
10 m away, elevation 60°. Height —
💡 Hint:
tan 60 = √3.
Explanation:
10√3 m.
True or false
0/81
Depression is below the horizontal.
Explanation:
True.
2
At 45° the height of the tower equals the distance.
Explanation:
True — tan = 1.
3
tan is enough for the height of a rope, even when the rope is the hypotenuse.
Explanation:
False — a hypotenuse uses sin.
4
The full height of a broken tree is only the stump.
Explanation:
False — add the broken part too.
5
The angle of elevation increases as you move closer.
Explanation:
True.
6
The angle of depression is placed in the corner between the tower and the line of sight.
Explanation:
False — it equals the corner on the ground.
7
At 30 m and 30°, the height is 10√3 m.
Explanation:
True.
8
If the eye is at 1.5 m, the triangle height of a 30 m building stays 30 m.
Explanation:
False — 28.5 m.
Fill in the blanks
0/81
tan = height / ______.
💡 Hint:
Distance.
Explanation:
The adjacent side.
2
At 20 m and 45° the height is ______ m.
💡 Hint:
20 m.
Explanation:
tan 45 = 1.
3
A 10 m rope at 30°. Height ______ m.
💡 Hint:
5 m.
Explanation:
Half.
4
The full height of the broken tree at 6 m and 30° is ______ m.
💡 Hint:
6√3 m.
Explanation:
2√3 + 4√3.
5
Walk 10 m from 30° to 60°. Distance left ______ m.
💡 Hint:
5 m.
Explanation:
Half.
6
A 12 m roof, depression 30°. Distance ______ m.
💡 Hint:
12√3 m.
Explanation:
12 × √3.
7
sin 60° = ______.
💡 Hint:
√3/2.
Explanation:
The table.
8
At 40 m and 45° the boat is ______ m away.
💡 Hint:
40 m.
Explanation:
tan 45 = 1.
Match
0/21
Match the situation with the ratio.
Column B: A. distance / cos · B. height = distance × tan · C. height = length × sin · D. same angle on the ground
1. Tower, distance known
2. Rope as hypotenuse
3. Depression
4. Broken part
Explanation:
A tower uses tan, a rope uses sin, depression equals the ground angle, and the broken part is distance/cos.
2
Match the part of exercise 9.1 with its shape.
Column B: A. The angle comes down to the ground · B. sin, hypotenuse given · C. stump + hypotenuse · D. tan, distance given
1. The rope question
2. The broken tree
3. One tower
4. Depression from a roof
Explanation:
The rope uses sin, the tree is a sum, the tower uses tan, and depression uses parallel horizontals.
Assertion–reason
0/5Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): At 20 m and 45° the tower is 20 m high.
Reason (R): tan 45° = 1, so height = distance.
Explanation:
Both are true and R is the reason.
2
Assertion (A): Depression is below the horizontal.
Reason (R): tan 30° = 1/√3.
Explanation:
Both are true, but R is not the definition of depression.
3
Assertion (A): A 10 m rope at 30° gives a 5 m pole.
Reason (R): The rope is the adjacent side.
Explanation:
A is true. R is false, the rope is the hypotenuse.
4
Assertion (A): At 6 m and 30° the full height of the broken tree is only 2√3 m.
Reason (R): The stump = distance × tan of the angle, and the broken part is a separate hypotenuse.
Explanation:
A is false, the full height is 6√3 m. R is true.
5
Assertion (A): From a 12 m roof at a depression of 30°, the distance is 12√3 m.
Reason (R): Because the horizontals are parallel, the ground angle is also 30° and tan 30° = 12/d.
Explanation:
Both are true and R is the basis of the calculation.
Coefficient practice
0/4These chemistry lines are not a result of this maths chapter. They are only practice in filling coefficients. A blank means 1.
1
This is coefficient practice and not a result of this maths chapter. In the line where H2 + O2 makes water, Fill coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
2
This is coefficient practice and not a result of this maths chapter. In the line where N2 + H2 makes ammonia, Fill coefficients (blank = 1).
N2 + H2 → NH3
Explanation: N2 + 3H2 → 2NH3
3
This is coefficient practice and not a result of this maths chapter. In the line where C + O2 makes carbon dioxide, Fill coefficients (blank = 1).
C + O2 → CO2
Explanation: C + O2 → CO2
4
This is coefficient practice and not a result of this maths chapter. In the burning line of CH4 + O2, Fill coefficients (blank = 1).
CH4 + O2 → CO2 + H2O
Explanation: CH4 + 2O2 → CO2 + 2H2O
Classify
0/21
Place each view as elevation or depression.
The top of a tower from the ground
A person on the road, seen from a roof
A flower pot below, seen from a balcony
A kite seen from the field
Explanation:
Looking up is elevation. Looking down is depression.
2
Place each job with the right ratio.
Distance known, height asked
Rope length known, height asked
Both the stump and the broken part
Eye 1.5 m, building 30 m
Explanation:
Distance uses tan, a rope uses sin, a tree uses a sum, and the eye height is subtracted.
Very short answer
0/51
Define the angle of elevation in one line.
Model answer (board format)
The angle the line of sight makes above the horizontal.
Check your answer:
2
Define the angle of depression in one line.
Model answer (board format)
The angle the line of sight makes below the horizontal.
Check your answer:
3
Write the tan relation of height and distance.
Model answer (board format)
tan of the angle = height / distance, when the angle is on the ground.
Check your answer:
4
Write the height formula when the rope is the hypotenuse.
Model answer (board format)
Height = length × sin of the angle.
Check your answer:
5
In a calculation, which corner holds the angle of depression?
Model answer (board format)
In the ground corner, because the two horizontals are parallel.
Check your answer:
Short answer
0/41
The elevation is 60° from a point 12 m from the foot. Find the height.
Model answer (board format)
tan 60° = h/12. √3 = h/12. h = 12√3 m.
Check your answer:
2
An 8 m rope makes 30° with the ground. Find the height and the ground distance.
Model answer (board format)
Height = 8 × 1/2 = 4 m. Distance = 8 × √3/2 = 4√3 m.
Check your answer:
3
From a 40 m cliff the depressions of two boats are 45° and 30°, on one side. Find the distance between them.
Model answer (board format)
Nearer 40 m, farther 40√3 m. The gap is 40(√3 − 1) m.
Check your answer:
4
Walking 15 m closer changes the angle from 30° to 60°. Find the height.
Model answer (board format)
x+15 = 3x, x = 7.5 m. h = 7.5√3 m.
Check your answer:
Long answer
0/31
A pole is 18 m away at an elevation of 30°. Find the height. Then, if the angle becomes 60° and the height stays the same, what distance remains?
Model answer (board format)
h = 18 × 1/√3 = 6√3 m. At 60°, tan 60 = 6√3 / d. √3 = 6√3 / d. d = 6 m.
Check your answer:
2
A tree breaks. The touch distance is 9 m and the angle is 30°. Find the stump, the broken part and the full height.
Model answer (board format)
Stump = 9/√3 = 3√3 m. Broken part = 9/(√3/2) = 6√3 m. Full height = 9√3 m.
Check your answer:
3
From the eye of a 1.2 m girl a balloon is first at 60° and later at 30°. The height above the eye stays 30√3 m. How far did the balloon move?
Model answer (board format)
tan 60 = 30√3 / x, so x = 30 m. tan 30 = 30√3 / (x+d). 1/√3 = 30√3 / (30+d). 30+d = 90. d = 60 m. The girl’s 1.2 m adds into the height of the balloon from the ground, but the gap d comes from this triangle.
Check your answer:
BSEB model paper · practice
0/6This model set is for practice. It is not a question from any year’s annual examination.
1
If the elevation is 45° from 25 m away on the ground, the height is —
💡 Hint:
tan 45 = 1.
Explanation:
25 m.
2
A 6 m rope at 30° gives a pole of height —
💡 Hint:
Half.
Explanation:
3 m.
3
Distance 9 m, angle 30°, the full height of the broken tree is ______ m.
💡 Hint:
9√3 m.
Explanation:
3√3 + 6√3.
4
A roof is 8 m high. The depression of a point is 45°. Find the distance.
Model answer (board format)
The ground angle is 45°. tan 45° = 8/d. d = 8 m.
Check your answer:
5
The elevation is 30° from 30 m away from the foot of a tower. Find the height. Then where will 60° occur for the same height?
Model answer (board format)
h = 30/√3 = 10√3 m. At 60°, √3 = 10√3 / d, so d = 10 m. That is 10 m from the foot.
Check your answer:
6
Assertion (A): The angle of elevation increases as you move closer.
Reason (R): Depression and elevation are two names for the same view.
Explanation:
A is true. R is false. One is upward, the other is downward.
CBSE-style questions
0/6These are competency-based practice questions. They are not a copy of any year’s paper.
1
A student writes the height of a 10 m rope at 30° as 10/√3 m. The miss is —
💡 Hint:
The rope is the hypotenuse.
Explanation:
The correct height is 10 × sin 30° = 5 m. 10/√3 is the tan answer.
2
The walk is 20 m on one side, from 30° to 60°. The distance left is —
💡 Hint:
x+20 = 3x.
Explanation:
10 m. The height is 10√3 m.
3
Assertion (A): Boats at 45° and 30° from a 40 m cliff are 40(√3 − 1) m apart.
Reason (R): At 45° the distance equals the height, and at 30° the distance is the height × √3.
Explanation:
Both are true. 40√3 − 40 = 40(√3 − 1).
4
Assertion (A): The angle of depression is placed between the wall of the tower and the line of sight.
Reason (R): Because the horizontals are parallel, this angle equals the corner on the ground.
Explanation:
A is false. R is true.
5
A circus rope is 16 m and makes 30° with the ground. Find the height of the pole and the distance from the foot to the tie point.
Model answer (board format)
Height = 16 × 1/2 = 8 m. Distance = 16 × √3/2 = 8√3 m.
Check your answer:
6
A 1.5 m boy looks at a 21.5 m building. What height do you use in the triangle, and if he is 20 m away at 45°, does the height match?
Model answer (board format)
The triangle height is 21.5 − 1.5 = 20 m. At 45°, tan = 1, so 20 m away gives a height of 20 m. Yes, it matches.
Check your answer:
🏛️ Board exam corner — Bihar Board (BSEB)— CBSE
Switch board with BSEB | CBSE above. The lessons follow the same NCERT chapter.
BSEB model · practiceBoard tip
This page has no verified annual-exam question, because no source page has been added. The model set below is practice in the board pattern.
🏛️ Model questions on one page →
The verified label will be used only when a source page for the question is available.
CBSE-style · competency-based
These are case and assertion-reason practice items. Do not treat them as past CBSE questions.
🔁 Spaced review — today’s questions
Wrong questions return soon; correct ones return after a few days.
🧠 What you learned + equation sheet
What you learned
- The line of sight runs from the eye to the point viewed.
- Head up means elevation, head down means depression.
- tan = height/distance when the angle is on the ground.
- A slanted rope is the hypotenuse, and height = length × sin of the angle.
- The height of a broken tree = stump + broken part.
- The angle of depression equals the angle at the ground corner.
| What | Keep this |
|---|---|
| Elevation | head up, above the horizontal |
| Depression | head down, below the horizontal |
| tan 30° | 1/√3 |
| tan 45° | 1 |
| tan 60° | √3 |
| sin 30° | 1/2 |
The notes are original writing. The textbook was used only for activity order and numbers. “Verified” will be used only on a question that has a source page.