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 12 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
	17 min 25 sec 18 min 26 sec 15 min 23 sec 16 min 24 sec 13 min 22 sec

Question 2

2.	A man 1.9 m tall stands at a distance of 7.4 m from a lamp post and casts a shadow of 1.3 m on the ground. Find the height of the lamp post .
	9.72 m 17.72 m 7.72 m 15.72 m 12.72 m

Question 3

3.	Two boys are on opposite sides of a tower of 170 m height. They measure the angle of elevation of the top of the tower as 30° and 60° respectively. Find the distance between the two boys.
	680 3 √ 3 m 680 3 m 340 √ 2 m 680 3 √ 18 m 680 m

Question 4

4.	If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?
	∠a ∠b ∠d ∠c

Question 5

5.	The angles of depression of two boats from the top of a cliff 160 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
	393.52 m 369.52 m 354.52 m 376.52 m 356.52 m

Question 6

6.	There are two temples one on each bank of a river, just opposite to each other. One of the temples is 200 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 60° respectively. Find the height of the other temple.
	149.33 m 108.33 m 129.33 m 133.33 m 150.33 m

Question 7

7.	A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the building is 7 m, find the height of the flag staff .
	7.12 m 3.12 m 5.12 m 4.12 m 6.12 m

Question 8

8.	The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 190 m from the foot of the tree . Find the height of the tree before it was broken.
	709.10 m 714.10 m 686.10 m 731.10 m 693.10 m

Question 9

9.	A flagstaff stands on the top of a building at a distance of 30 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 45°. Find the height of the flagstaff .
	1800 m ( 30 √ 3 − 30 ) m ( 45 √ 2 − 15 √ 6 ) m ( 30 √ 18 − 30 √ 6 ) m ( 2 − √ 3 ) m

Question 10

10.	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 60° . If the distance between the point and the foot of the building is 110 m , find the height of the building .
	110 √ 18 m 165 √ 2 m 330 m 110 m 110 √ 3 m

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