Chapter 9 · Class 10 CBSE · MCQ Test

Some Applications of Trigonometry MCQ Test — Class 10 CBSE

Practice 10 multiple-choice questions with instant answer reveal and explanations.

Some Applications of Trigonometry — MCQ Questions

1Which of the following statements correctly defines the angle of elevation?

A.The angle formed by the line of sight with the vertical line, when the object is above the horizontal level.
B.The angle formed by the line of sight with the horizontal line, when the object is above the horizontal level.
C.The angle formed by the line of sight with the horizontal line, when the object is below the horizontal level.
D.The angle formed between the observer's eye and the top of the object.
Show Answer+

Answer: The angle formed by the line of sight with the horizontal line, when the object is above the horizontal level.

Hint: Remember that both angle of elevation and depression are always measured with respect to a horizontal line.

Solution:

The angle of elevation is defined as the angle formed by the line of sight with the horizontal line when the observer looks upwards at an object.

This means the object is above the horizontal level of the observer's eye.

2A person standing on a 50 m high cliff observes a boat in the sea. The angle of depression of the boat is formed by the line of sight and:

A.the vertical line from the observer's eye to the sea.
B.the horizontal line above the line of sight.
C.the line connecting the base of the cliff to the boat.
D.the horizontal line at the level of the sea.
Show Answer+

Answer: the horizontal line above the line of sight.

Hint: Just like the angle of elevation, the angle of depression is also measured from a horizontal line. Consider where the observer's horizontal line would be.

Solution:

The angle of depression is formed when an observer looks downwards at an object.

It is the angle between the horizontal line (at the observer's eye level) and the line of sight to the object.

Therefore, the angle of depression is formed by the horizontal line above the line of sight to the boat.

3A boy is standing on the ground and looking at the top of a 10-meter tall tree. His eye level is 1.5 m above the ground. If the angle of elevation of the top of the tree from his eye is 45°, what is the horizontal distance between the boy and the tree?

A.10 m
B.8.5 m
C.11.5 m
D.1.5 m
Show Answer+

Answer: 8.5 m

Hint: Remember that the angle of elevation is measured from the eye level of the observer. Adjust the height of the tree accordingly for the right-angled triangle.

Solution:

Let the height of the tree be H = 10 m and the eye level of the boy be h = 1.5 m.

The height of the tree above the boy's eye level will be H' = H - h = 10 m - 1.5 m = 8.5 m.

Let 'd' be the horizontal distance between the boy and the tree. The angle of elevation is 45°.

In the right-angled triangle formed, tan(45°) = Opposite / Adjacent = H' / d. Since tan(45°) = 1, we have 1 = 8.5 / d, so d = 8.5 m.

4Ravi is trying to find the height of a building. He is standing at a point A on the ground and observes the top of a building at point B. He incorrectly draws the angle of depression from B to A as the angle between the line BA and the vertical line passing through B. What is the correct way to represent the angle of depression from B to A (assuming A is on the ground, B is the top of the building)?

A.The angle between the line BA and the line segment AC, where C is the foot of the building.
B.The angle between the horizontal line through B and the line of sight BA.
C.The angle between the line BA and the line segment BC, where C is the foot of the building.
D.The angle at point A formed by the line BA and the horizontal ground.
Show Answer+

Answer: The angle between the horizontal line through B and the line of sight BA.

Hint: The angle of depression is always measured from a horizontal line at the observer's position, looking down towards the object.

Solution:

The angle of depression is an angle formed by the horizontal line from the observer's eye level and the line of sight when looking downwards.

In this scenario, B is the observer's position (top of the building), and A is the object (point on the ground).

Therefore, the correct angle of depression is between the horizontal line passing through B (parallel to the ground) and the line of sight BA.

5The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. The height of the tower is:

A.30√3 m
B.10√3 m
C.30 m
D.15 m
Show Answer+

Answer: 10√3 m

Hint: Consider the right-angled triangle formed by the tower, the ground, and the line of sight. Which trigonometric ratio relates the opposite side (height) to the adjacent side (distance)?

Solution:

Let 'h' be the height of the tower and 'd' be the distance from the foot of the tower, d = 30 m.

The angle of elevation (θ) is 30°.

In the right-angled triangle, tan(θ) = Opposite / Adjacent = h / d.

So, tan(30°) = h / 30. We know tan(30°) = 1/√3. Therefore, 1/√3 = h / 30. Solving for h gives h = 30/√3 = (30√3) / (√3 × √3) = 30√3 / 3 = 10√3 m.

6A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, what is the height of the wall?

A.15√3 m
B.15/√2 m
C.7.5 m
D.15 m
Show Answer+

Answer: 7.5 m

Hint: Be careful with the angle given. It's with the wall, not the ground. Identify which trigonometric ratio relates the hypotenuse (ladder length) to the adjacent side (height of the wall) for the given angle.

Solution:

Let 'L' be the length of the ladder, L = 15 m. Let 'h' be the height of the wall.

The angle (θ) the ladder makes with the wall is 60°. This means 'h' is the side adjacent to the angle 60° and 'L' is the hypotenuse.

Using the cosine ratio: cos(θ) = Adjacent / Hypotenuse = h / L.

So, cos(60°) = h / 15. We know cos(60°) = 1/2. Therefore, 1/2 = h / 15. Solving for h gives h = 15 / 2 = 7.5 m.

7An observer is standing at a certain distance from a pole. If the observer moves further away from the pole, what happens to the angle of elevation of the top of the pole from the observer's eye?

A.It increases.
B.It decreases.
C.It remains the same.
D.It first increases then decreases.
Show Answer+

Answer: It decreases.

Hint: Imagine drawing the triangle. As the base length (distance from the pole) increases while the height remains constant, what happens to the angle at the observer's position?

Solution:

Consider a right-angled triangle where the height is constant (pole height) and the base is the distance from the observer to the pole.

As the observer moves further away, the base of the triangle increases.

For a fixed height, as the base increases, the angle formed at the observer's position (angle of elevation) must decrease.

8A kite is flying at a height of 60 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 60°. Assuming there is no slack in the string, the length of the string is:

A.60√3 m
B.30√3 m
C.40√3 m
D.120 m
Show Answer+

Answer: 40√3 m

Hint: Form a right-angled triangle. The height is opposite the angle of inclination, and the string length is the hypotenuse. Which trigonometric ratio relates these two?

Solution:

Let 'h' be the height of the kite, h = 60 m. Let 'L' be the length of the string (hypotenuse).

The angle of inclination (θ) is 60°.

In the right-angled triangle, sin(θ) = Opposite / Hypotenuse = h / L.

So, sin(60°) = 60 / L. We know sin(60°) = √3/2. Therefore, √3/2 = 60 / L. Solving for L gives L = 60 × 2 / √3 = 120 / √3.

To rationalize the denominator, L = (120√3) / (√3 × √3) = 120√3 / 3 = 40√3 m.

9The line of sight is defined as:

A.The horizontal line from the observer's eye.
B.The vertical line from the observer's eye to the object.
C.The line drawn from the eye of an observer to the object being viewed.
D.The path followed by light rays from the observer to the object.
Show Answer+

Answer: The line drawn from the eye of an observer to the object being viewed.

Hint: Think about what connects the observer's eye directly to the object they are looking at.

Solution:

In the context of 'Some Applications of Trigonometry,' the line of sight is a straight line.

It is imagined or drawn directly from the eye of the observer to the object that the observer is looking at.

10To find the height of a vertical pole when the distance from its base and the angle of elevation of its top are known, one should directly use the _______ trigonometric ratio.

A.sine
B.cosine
C.tangent
D.cosecant
Show Answer+

Answer: tangent

Hint: Consider the sides of the right-angled triangle: the height is opposite the angle, and the distance from the base is adjacent to the angle.

Solution:

Let 'h' be the height of the pole (opposite side to the angle of elevation).

Let 'd' be the distance from the base (adjacent side to the angle of elevation).

The tangent ratio directly relates the opposite side and the adjacent side: tan(angle) = Opposite / Adjacent = h / d. Therefore, the tangent ratio is the most direct choice.

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Tips for Some Applications of Trigonometry MCQs

  • 1Read each question carefully and identify what is being asked before looking at the options.
  • 2Try to solve the problem mentally or on paper first, then match your answer with the options.
  • 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
  • 4Check units, signs, and edge cases — these are common traps in Some Applications of Trigonometry MCQs.
  • 5Review your mistakes after completing the test to build lasting understanding.

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