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Class 10 Maths Chapter 9: Some Applications of Trigonometry MCQs with answers

10 multiple-choice questions on Some Applications of Trigonometry, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
The angle of elevation of the top of a mobile tower, seen by an observer, is the angle between
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Answer: (a) the line of sight and the horizontal through the observer's eye

Both angles of elevation and depression are measured from the horizontal through the eye, up to the line of sight. Option (d) measures from the vertical, which is the usual slip.

Question 2
Meena, standing on her balcony, looks down at a scooter parked on the road. The angle between her line of sight and the horizontal through her eye is called the
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Answer: (b) angle of depression

The scooter is below the horizontal level of her eye, so the angle her line of sight makes with the horizontal is an angle of depression.

Question 3
The line drawn from the eye of an observer to the point of the object being viewed is called the
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Answer: (c) line of sight

By definition this line is the line of sight; the angles of the chapter are measured between it and the horizontal.

Question 4
From a point on level ground 18 m from the foot of a water tower, the angle of elevation of its top is 45°. The height of the water tower is
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Answer: (a) 18 m

tan 45° = height / 18 and tan 45° = 1, so the height is 18 m. (18√3 m comes from wrongly using tan 60°, 6√3 m from tan 30°.)

Question 5
An escalator in a metro station is 14 m long and makes an angle of 30° with the horizontal. The vertical height it lifts a passenger through is
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Answer: (c) 7 m

The escalator is the hypotenuse and the height is opposite the 30° angle, so height = 14 sin 30° = 14 × 1/2 = 7 m. 7√3 m is the horizontal run (cos 30°).

Question 6
To find the height of a chimney without climbing it, an observer of known eye height needs to measure
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Answer: (b) the distance from the foot of the chimney and the angle of elevation of its top

A height is found from one right triangle: the horizontal distance from the foot, the angle of elevation, and the observer's own height. An angle alone or a distance alone does not fix the triangle.

Question 7
From the top of a cliff, the angle of depression of a boat at sea is 30°. The angle of elevation of the top of the cliff, seen from the boat, is
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Answer: (b) 30°

In the right triangle formed by the cliff, the sea and the line of sight, the angle at the cliff-top is 90° − 30° = 60°, so the angle at the boat is 180° − 90° − 60° = 30°. The depression and the elevation are alternate angles, hence equal.

Question 8
A vertical pole casts a shadow on level ground equal to its own height. The angle of elevation of the Sun is
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Answer: (d) 45°

tan θ = height / shadow = 1, and tan 45° = 1, so θ = 45°.

Question 9
The height of a minaret and the length of its shadow on level ground are in the ratio √3 : 1. The angle of elevation of the Sun is
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Answer: (c) 60°

tan θ = height / shadow = √3, and tan 60° = √3, so θ = 60°. (30° is what one gets by inverting the ratio.)

Question 10
In a heights problem, the horizontal distance d from the foot of a tower and the angle of elevation θ of its top are known, and the height h is wanted. The ratio to use is
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Answer: (b) tan θ = hd

h is the side opposite θ and d is the side adjacent to it; both are legs of the right triangle, so the ratio relating them is tan θ = h/d.

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