qpaper
Generate

Class 10 Maths Chapter 9: Some Applications of Trigonometry — Important Questions & Sample Paper

CBSE· 44+ original questions readyहिन्दी में देखें

Practise important & sample questions with answers, see the CBSE marks distribution & blueprint, or generate a full sample paper — free, for 2026-27.

Reviewed by qpaper's CBSE curriculum team · Edited by Mohit · Updated June 2026

Quick answer

Yes — this page has 44+ original Class 10 Mathematics Chapter 9 (“Some Applications of Trigonometry”) important questions with answers (Multiple Choice (MCQ), Assertion–Reason, Short Answer, Short Answer, Long Answer, Case Study). Practise them free, or generate a full CBSE board-pattern sample paper (80 marks) and export it to PDF or Word — in English & Hindi, for 2026-27.

Chapter 9 of CBSE Class 10 Mathematics, Some Applications of Trigonometry, shifts from abstract ratios to practical real-world measurements. The chapter revolves around finding heights of objects (buildings, poles, lighthouses) and distances between points (width of a river, distance of a ship) without direct measurement. It introduces two key ideas: the line of sight and the angles formed with the horizontal—angle of elevation when looking upward at an object, and angle of depression when looking downward from a higher point. Every problem reduces to constructing right triangles and applying trigonometric ratios (primarily tangent, as it connects the opposite and adjacent sides). Typical exam questions involve one or two such triangles. For instance, direct problems ask for the height of a tower given its shadow length and the sun’s altitude, or the distance of a ship from a lighthouse using a known angle of depression. More complex problems combine two observations, such as the angles from a point on the ground to the top of a statue and its pedestal separately (sample question 1), or the angles of depression of two ships in a line from a lighthouse to determine the distance between them or the lighthouse height. There are also speed‑time variations, like a boat approaching a cliff where the angle of depression changes from 30° to 60° in 6 minutes, requiring students to calculate the remaining time to reach shore. Success in this chapter depends on clear diagram drawing, correct identification of right triangles, and the ability to form and solve algebraic equations using tan, sin, or cos. These problems frequently carry 3–4 marks in CBSE board exams, making them essential for scoring well.

Generate a full sample paper for this chapter

Pick chapters, set your blueprint and marks distribution, and export a print-ready PDF or editable Word — with an answer key. Free to build.

Generate full paperSee a sample paper

Preview: a real paper we generate

This is the actual CBSE board-style layout you export — built from this chapter's own questions, with an answer key.

Mathematics — Some Applications of Trigonometry

Class 10Time: 3 hrsMax Marks: 80

SECTION A

  1. 1.

    A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. The distance he walked is:

    (a) 19√3 m(b) 19 m(c) 9.5√3 m(d) 28.5√3 m
    1
  2. 2.

    A kite is flying at a height of 50 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 45°. Assuming no slack in the string, the length of the string is:

    (a) 50√2 m(b) 50 m(c) 100 m(d) 50/√2 m
    1
  3. 3.

    A 1.6 m tall statue stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. The height of the pedestal is:

    (a) 0.8(√3 + 1) m(b) 1.6(√3 + 1) m(c) 0.8(√3 - 1) m(d) 1.6√3 m
    1

+ 41 more questions in the full paper

Generate full paper

Marks distribution & blueprint

In a CBSE exam, this chapter typically contributes questions across the following types. The last column shows how many original questions of each type we have ready in our bank for this chapter:

Question typeMarks eachIn our bank
Multiple Choice (MCQ)1 mark13
Assertion–Reason1 mark6
Short Answer2 marks8
Short Answer3 marks6
Long Answer5 marks5
Case Study4 marks6

44 original, exam-style questions in our bank for this chapter — with answers.

Important & sample questions (with answers)

Real, exam-style questions to practise and revise — each with its answer. Generate a full paper for unlimited more.

  1. Q1. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. The distance he walked is:

    1 mark
    Multiple Choice (MCQ)
    (A) 19√3 m(B) 19 m(C) 9.5√3 m(D) 28.5√3 m
    ▸ Answer

    19√3 m

  2. Q2. A kite is flying at a height of 50 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 45°. Assuming no slack in the string, the length of the string is:

    1 mark
    Multiple Choice (MCQ)
    (A) 50√2 m(B) 50 m(C) 100 m(D) 50/√2 m
    ▸ Answer

    50√2 m

  3. Q3. A 1.6 m tall statue stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. The height of the pedestal is:

    1 mark
    Multiple Choice (MCQ)
    (A) 0.8(√3 + 1) m(B) 1.6(√3 + 1) m(C) 0.8(√3 - 1) m(D) 1.6√3 m
    ▸ Answer

    0.8(√3 + 1) m

  4. Q4. From the top of a 100 m high lighthouse, the angles of depression of two ships on the same side of the lighthouse are 45° and 30°. If the ships are in a line with the foot of the lighthouse, the distance between the ships is:

    1 mark
    Multiple Choice (MCQ)
    (A) 100(√3 - 1) m(B) 100(√3 + 1) m(C) 100√3 m(D) 100 m
    ▸ Answer

    100(√3 - 1) m

  5. Q5. Assertion (A): The angle of depression of a boat from the top of a 75 m high lighthouse is 30°. The distance of the boat from the lighthouse is 75√3 m. Reason (R): tan 30° = 1/√3.

    1 mark
    Assertion–Reason
    (A) Both A and R are true and R is the correct explanation of A.(B) Both A and R are true but R is not the correct explanation of A.(C) A is true but R is false.(D) A is false but R is true.
    ▸ Answer

    Both A and R are true but R is not the correct explanation of A.

  6. Q6. The angle of elevation of a cloud from a point 60 m above a lake is 30°, and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud above the lake surface.

    2 marks
    Short Answer
    ▸ Answer

    120 m

  7. Q7. A ladder 10 m long leans against a wall making an angle of 60° with the ground. How high up the wall does the ladder reach?

    2 marks
    Short Answer
    ▸ Answer

    5√3 m (or 8.66 m)

  8. Q8. A vertical bridge over a river is at a constant height of 4 m above the water level. From a point on the bridge, the angles of depression of the two opposite banks of the river are 30° and 45°. Find the width of the river.

    3 marks
    Short Answer
    ▸ Answer

    4(1 + √3) m

  9. Q9. A man on a cliff observes a boat approaching the shore directly below him at a uniform speed. Initially, the angle of depression of the boat is 30°, and 6 minutes later it becomes 60°. How much more time will the boat take to reach the shore?

    3 marks
    Short Answer
    ▸ Answer

    3 minutes

  10. Q10. A tree breaks due to a storm and the broken part bends so that the top touches the ground making an angle of 30° with the ground. The distance from the foot of the unchanged stump to the point where the top touches the ground is 8 m. Find the original height of the tree.

    5 marks
    Long Answer
    ▸ Answer

    The original height of the tree is 8√3 m.

  11. Q11. The angles of depression of two ships from the top of a lighthouse are 30° and 45° respectively. The ships are in the same straight line with the lighthouse, one exactly behind the other on the same side. If the distance between the ships is 100 m, find the height of the lighthouse.

    5 marks
    Long Answer
    ▸ Answer

    The height of the lighthouse is 50(√3 + 1) m.

  12. Q12. In a park, a statue is mounted on a 2-metre high pedestal. From a point on the ground, the angle of elevation of the top of the pedestal (which is the bottom of the statue) is 45°, and the angle of elevation of the top of the statue is 60°.

    4 marks
    Case Study
    1. (i) Find the distance of the point from the pedestal.2 marks
    2. (ii) Calculate the height of the statue.2 marks
    ▸ Answer

    Distance = 2 m; Height of statue = 2(√3 - 1) m

Frequently asked questions

What is the difference between angle of elevation and angle of depression?

Both are measured from the horizontal. Angle of elevation is when you look up from the horizontal line of sight to an object above; angle of depression is when you look down from the horizontal to an object below.

Which trigonometric ratio is most commonly used in height and distance problems, and why?

The tangent (tan) ratio is most common because it directly relates the opposite side (height) and the adjacent side (horizontal distance) without needing the hypotenuse. Problems often give or ask for these two measures.

How do I solve problems with two different angles of elevation/depression?

Draw two right triangles sharing the same vertical height. Assign a variable to the unknown distance(s). Use tan of each angle to write equations linking height and distance, then solve algebraically. Many problems involve a common height and two different horizontal distances.

How to approach a boat approaching a cliff or lighthouse problem with time and speed?

The height of the cliff/lighthouse is constant. Use the two angles of depression (initial and after some time) to find the distance travelled in that time. Then calculate speed = distance/time. To find the remaining time, use the initial or final position distance and the same speed to reach the shore.

More chapters