Some Applications of Trigonometry — Class 10 MCQs with Answers

Some Applications of Trigonometry — important questions & MCQs with answers (Class 10 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Angle of elevation is measured from:

   A.Vertical, downward

   B.Object to ground

   C.Horizontal, upward to object✓ Correct

   D.Ground to ground

   Answer: C. Horizontal, upward to object

   Explanation: Angle of elevation is the angle a horizontal line of sight makes turning upward to sight an object above it — measuring from the vertical, not the horizontal, is the usual mix-up.

2. Q2Easy

   tan 45° =

   A.0

   B.1/√3

   C.√3

   D.1✓ Correct

   Answer: D. 1

   Explanation: In a right triangle with a 45° angle, opposite and adjacent sides are equal, so tan 45° = opposite/adjacent = 1 — not √3 (tan 60°) or 1/√3 (tan 30°).

3. Q3Easy

   The angle of elevation of an object is measured:

   A.Downward from horizontal

   B.Upward from horizontal✓ Correct

   C.From the ground straight up

   D.From the vertical

   Answer: B. Upward from horizontal

   Explanation: The angle of elevation is the angle between the horizontal line of sight and the upward line to an object above it — confusing it with the angle of depression, measured downward, is the common slip.

4. Q4Easy

   The angle of depression is:

   A.Equal to angle of elevation always

   B.Above the horizontal

   C.Below the horizontal✓ Correct

   D.90°

   Answer: C. Below the horizontal

   Explanation: The angle of depression is the angle the horizontal line of sight turns downward through to view an object below — by alternate angles it equals the elevation angle seen from that lower point.

5. Q5Easy

   The line drawn from the eye of an observer to a point on the object being viewed is called the:

   A.Line of sight✓ Correct

   B.Angle of elevation

   C.Angle of depression

   D.Horizontal line

   Answer: A. Line of sight

   Explanation: The line of sight joins the observer's eye to the point being viewed.

6. Q6Easy

   The angle of elevation of the top of a tower from a point 30 m from its foot is 45°. The height of the tower is:

   A.15 m

   B.30 m✓ Correct

   C.30√3 m

   D.60 m

   Answer: B. 30 m

   Explanation: The height is 30 tan 45° = 30 m.

7. Q7Medium

   The angle of elevation and the angle of depression measured between the same two points are:

   A.Complementary

   B.Equal, being alternate angles with the horizontal✓ Correct

   C.Always 90° apart

   D.Supplementary

   Answer: B. Equal, being alternate angles with the horizontal

   Explanation: The two horizontals are parallel, so the angle of elevation from the lower point equals the angle of depression from the upper point.

8. Q8Medium

   Tower casts a shadow 10 m long when sun's elevation is 60°. Height of tower:

   A.20 m

   B.10/√3 m

   C.10 m

   D.10√3 m✓ Correct

   Answer: D. 10√3 m

   Explanation: Right triangle with the shadow as base: tan 60° = opposite/adjacent = h/10, and tan 60° = √3, so h = 10√3 m — not 10/√3, which mixes up tan 30° instead.

9. Q9Medium

   From two points 30 m apart on the same side of a tower, the angles of elevation of the top of the tower are 30° and 60°. The height of the tower is:

   A.15 m

   B.30 m

   C.15√3 m✓ Correct

   D.30√3 m

   Answer: C. 15√3 m

   Explanation: Let height h, distance from foot to closer point d. tan 60° = h/d ⇒ d = h/√3. tan 30° = h/(d + 30) ⇒ (d + 30) = h√3. So h/√3 + 30 = h√3 ⇒ 30 = h√3 − h/√3 = (2h/√3) ⇒ h = 15√3.

10. Q10Medium

    From the top of a tower 20 m high, the angles of depression of two points on the ground (on the same side) are 30° and 45°. Distance between the two points is:

    A.20(√3 − 1) m✓ Correct

    B.20√3 m

    C.20 m

    D.20(√3 + 1) m

    Answer: A. 20(√3 − 1) m

    Explanation: Far point: 20/tan 30° = 20√3. Close point: 20/tan 45° = 20. Distance = 20√3 − 20 = 20(√3 − 1).

11. Q11Medium

    A ladder makes 60° with ground, foot 2.5 m from wall. Length of ladder:

    A.2.5 m

    B.5 m✓ Correct

    C.5√3 m

    D.10 m

    Answer: B. 5 m

    Explanation: Foot-to-wall distance is adjacent to the 60° ground angle, so use cosine: cos60° = 2.5/L. Since cos60° = 1/2, L = 5 m. A frequent mistake is applying sine here, meant for the opposite side.

12. Q12Hard

    Cliff is 100 m high. Boat at 45° depression is at distance:

    A.50 m

    B.100√2 m

    C.100 m✓ Correct

    D.100/√3 m

    Answer: C. 100 m

    Explanation: By alternate angles the boat's elevation angle also is 45°, so tan 45° = 100/d = 1, giving d = 100 m — the height-equals-distance shortcut at 45°.

13. Q13Hard

    From a 30 m tower, angle of depression of a car is 30°. Distance of car from base:

    A.30√3 m✓ Correct

    B.30 m

    C.10√3 m

    D.60 m

    Answer: A. 30√3 m

    Explanation: By alternate angles, the elevation from the car equals the 30° depression, so tan 30° = 30/d, and tan 30° = 1/√3, giving d = 30√3 m.

14. Q14Hard

    Two ships are sailing in the sea on either side of a lighthouse. The angles of depression of the two ships as observed from the top of the lighthouse are 60° and 45° respectively. If the height of the lighthouse is 100 m, the distance between the two ships is:

    A.100 m

    B.100(√3 + 3)/3 m✓ Correct

    C.100√3 m

    D.200 m

    Answer: B. 100(√3 + 3)/3 m

    Explanation: From top, depression 60° toward one ship: d₁ = 100/tan 60° = 100/√3. Other side, 45°: d₂ = 100. Distance = d₁ + d₂ = 100/√3 + 100 = 100(1 + 1/√3) = 100(√3 + 1)/√3 = 100(√3 + 1)·√3/3 = 100(3 + √3)/3.

Some Applications of Trigonometry — FAQs

More Class 10 Mathematics chapters

• 01Real Numbers
• 02Polynomials
• 03Pair of Linear Equations in Two Variables
• 04Quadratic Equations
• 05Arithmetic Progressions
• 06Triangles

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