SSC Board Practice

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SSC Grade X - Applications of Trigonometry

Question 1

1.	A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 8 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
	13 min 59 sec 7 min 53 sec 10 min 56 sec 11 min 57 sec 9 min 55 sec

Question 2

2.	There are two temples one on each bank of a river, just opposite to each other. One of the temples is 30 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the width of the river .
	30.00 m 35.00 m 25.00 m 27.00 m 33.00 m

Question 3

3.	A building stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the building is found to be 45° . If the distance between the point and the foot of the building is 10 m , find the distance between the observation point and the top of the building .
	20 √ 3 m 5 √ 12 m 10 √ 2 m 10 m 20 m

Question 4

4.	The angles of depression of two boats from the top of a cliff 190 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
	202.39 m 235.39 m 219.39 m 243.39 m 191.39 m

Question 5

5.	From the top of a light house which is 50 m high from the sea level, the angles of depression of two ships are 60° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
	57.73 m 60.73 m 52.73 m 62.73 m 54.73 m

Question 6

6.	From a point 160 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 45° and 30° respectively. Find the height of the cliff.
	92.38 m 95.38 m 87.38 m 97.38 m 89.38 m

Question 7

7.	If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?
	∠g ∠e ∠d ∠f

Question 8

8.	A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 30° and 45° and the distance between them is 190 m , find the height of the cliff.
	72.55 m 64.55 m 69.55 m 66.55 m 74.55 m

Question 9

9.	A tower stands vertically on the ground. The height of the tower is 90 m . The distance between the observation point and its foot is 90 m . Find the angle of elevation.
	60° 30° 75° 45° 105°

Question 10

10.	A radio tower stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the radio tower is found to be 45° . If the height of the radio tower is 170 m , find the distance between the observation point and the top of the radio tower .
	340 m 170 √ 2 m 340 √ 3 m 85 √ 12 m 170 m

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