CBSE Class 10 Maths Chapter-9 Some Applications of Trigonometry – Free PDF Download
Free PDF download of Important Questions with Answers for CBSE Class 10 Maths Chapter 9 – Some Applications of Trigonometry prepared by expert Maths teachers from latest edition of CBSE(NCERT) books only by CoolGyan to score more marks in CBSE board examination.
CBSE Class 10 Maths Chapter-9 Some Applications of Trigonometry Important Questions
CBSE Class 10 Maths Important Questions Chapter 9 – Some Applications of Trigonometry
1 Mark Questions
1. A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 
and the angle of depression of the base of the hill as 
. Calculate the distance of the hill from the ship and the height of the hill.
Ans. Let AB be the ship and CD be the hill.
Let BD = x m
In right 
In right 
Height of the hill = h + 10
= 30 +10 = 40 m
2. A boy is standing on the ground and flying a kite with 100 m of string at an elevation of . Another boy is standing on the roof of a 20 m high building and is flying his kite at
an elevation of 
. Both the boys are on the opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.
Ans. AE = 100 m (Given) and DC = 20 m (Given)
Let EF = h m
In right 
ABE,
Now in right 
3. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is. At a point Y, 40 m vertically above X, the angle of elevation is , find the height of the tower PQ and the distance XQ.
Ans. In right 
In right 
In right
4. At the foot of a mountain the elevation of its summit is . After ascending 1000 m towards the mountain up a slope of inclination, the elevation is found to be . Find the height of the mountain.
Ans. In right 
In right 
In right 
5. If the angles of elevation of the top of a tower from two points at distances a and b from the base and in the same straight line with it are complementary, then the height of the tower is
(a) 
(b) ab
(c) 
(d) 
Ans. a)
6. If the height of tower is half the height of the flagstaff on it and the angle of elevation of the top of the tower as seen from a point on the ground is 30
, then the angle of elevation of the top of the flagstaff as seen from the same point is
(a) 30
(b)45
(c) 60
(d) 90
Ans. (b)45
7. As observed from the top of a 75 m tall lighthouse the angles of depression of two ships are 30and 45. If one ship is exactly behind the other on the same side of the light house, then distance between the two ships is
(a)
(b) 
(c) 75
(d) 
Ans. (a)
8. The angle of elevation of the top a building from the foot of the tower is 30and the angle of elevation of the top of the tower from the foot of the building is 60. If the tower is 50 m high, then the height of the building is
(a) 50
(b) 
(c) 
(d) 
Ans. (b)
9. A 1.6 m tall girl stands at a distance of 3.2 m from a lamp post and casts a shadow of 4.8 m on the ground, then the height of the lamp post is
(a) 
(b)
(c) 
(d) 
Ans. (a)
10. A tree breaks due to storm and broken part bends so that the top of the tree touches the ground making an angle of 30with ground. If the distance between the foot of the tree to the point where the top touches the ground is 8 m, then the height of the tree is
(a)
(b)
(c)
(d) 
Ans. (c)
11. The angle of elevation of the sun when the length of the shadow of a pole is 
times, then height of the pole is
(a) 30
(b) 45
(c) 60
(d) 75
Ans. (a) 30
12. From the figure, the angle of elevation 
is
(a) 30
(b) 60
(c) 45
(d) 75
Ans. (b) 60
13. A person walking 20 m towards a chimney in a horizontal line through its bare observer that its angle of elevation changes from 30to 45, then height of chimney is
(a) 
(b) 
(c) 
(d) 
Ans. (b)
14. Find height of the tower if length of shadow = 10 m and sun’s altitude = 45.
(a) 10 m
(b) 12 m
(c) 20 m
(d) none of these
Ans. (a) 10 m
15. If the angles of elevation of a tower from two points at distances a and b where a > b, from its foot and in the same straight line from it are 30 and 60, then height of the tower is
(a) 
(b)
(c) 
(d)
Ans. (b)
16. The 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, then height of tower is
(a) 10 m
(b) 
m
(c) 
m
(d) 
m
Ans. (a) 10 m
17. If height of the tower = shadow of the tower, then angle of elevation is
(a) 30
(b) 45
(c) 60
(d) 90
Ans. (b) 45
18. If length of shadow = 20 m and angle of elevation = 60. Then height of tower is
(a) 20 m
(b) 
(c) 
(d) 
Ans. (d)
19. A little boy is flying a kite. The string of kite makes an angle of 30 with the ground. If length of the kite is h = 21 m, then length of string is
(a) 63 m
(b) 42 m
(c) 35 m
(d) 21 m
Ans. (b) 42 m
20. Line joining an eye and the object to be viewed is called
(a) Horizontal
(b) line of sight
(c) Vertical line
(d) None of these
Ans. (b) line of sight
