EduSahara™ Assignment
Name : Heights and Distances2
Chapter : Applications of Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Two boys are on opposite sides of a tower of 180 m height. They measure the angle of elevation of the top of the tower as 60° and 45° respectively. Find the distance between the two boys.
(i)
(
−
2
−
√
3
)
m
(ii)
(
60
√
3
+
180
)
m
(iii)
(
60
√
18
+
180
√
6
)
m
(iv)
(
−
21600
)
m
(v)
(
90
√
2
+
90
√
6
)
m
Question
2
2.
A person, walking 35 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .
(i)
(
105
2
√
6
+
35
2
√
18
)
m
(ii)
(
105
2
+
35
2
√
3
)
m
(iii)
(
2
+
√
3
)
m
(iv)
(
105
4
√
6
+
105
4
√
2
)
m
(v)
3675
2
m
Question
3
3.
A flagstaff stands on the top of a building at a distance of 25 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 .
(i)
(
2
−
√
3
)
m
(ii)
1250
m
(iii)
(
25
√
18
−
25
√
6
)
m
(iv)
(
75
2
√
2
−
25
2
√
6
)
m
(v)
(
25
√
3
−
25
)
m
Question
4
4.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 50 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 .
(i)
53.00 m
(ii)
45.00 m
(iii)
47.00 m
(iv)
55.00 m
(v)
50.00 m
Question
5
5.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 10 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 45° and 60° respectively. Find the height of the other temple.
(i)
5.23 m
(ii)
4.23 m
(iii)
3.23 m
(iv)
6.23 m
(v)
2.23 m
Question
6
6.
Two poles of equal height are standing opposite to each other on either side of a road which is 15 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .
(i)
height =
6.5 m
, distances away =
3.75 m
,
11.25 m
(ii)
height =
7.5 m
, distances away =
4.75 m
,
12.25 m
(iii)
height =
5.5 m
, distances away =
2.75 m
,
10.25 m
(iv)
height =
4.5 m
, distances away =
1.75 m
,
9.25 m
(v)
height =
8.5 m
, distances away =
5.75 m
,
13.25 m
Question
7
7.
From the top of a light house which is 40 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.
(i)
49.18 m
(ii)
43.18 m
(iii)
41.18 m
(iv)
46.18 m
(v)
51.18 m
Question
8
8.
From the top of a 9 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Find the height of the cable tower.
(i)
41.00 m
(ii)
33.00 m
(iii)
39.00 m
(iv)
36.00 m
(v)
31.00 m
Question
9
9.
The angle of elevation of the top of a building from the foot of a tower is 45°. The angle of elevation of the top of the tower from the foot of the building is 30°. If the height of the tower is 80 m, find the height of the building .
(i)
138.55 m
(ii)
132.55 m
(iii)
155.55 m
(iv)
160.55 m
(v)
110.55 m
Question
10
10.
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 45° and the angle of elevation of the top of the building is 30°. If the height of the building is 19 m, find the height of the flag staff .
(i)
13.91 m
(ii)
10.91 m
(iii)
8.91 m
(iv)
18.91 m
(v)
16.91 m
Question
11
11.
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 30°. If the height of the flag staff is 8 m, find the height of the building .
(i)
2.00 m
(ii)
6.00 m
(iii)
3.00 m
(iv)
4.00 m
(v)
5.00 m
Question
12
12.
From a point 170 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.
(i)
101.16 m
(ii)
98.16 m
(iii)
103.16 m
(iv)
93.16 m
(v)
95.16 m
Question
13
13.
From a point 110 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 pillar.
(i)
51.49 m
(ii)
43.49 m
(iii)
46.49 m
(iv)
41.49 m
(v)
49.49 m
Question
14
14.
The angles of depression of two boats from the top of a cliff 70 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
(i)
26.58 m
(ii)
24.58 m
(iii)
32.58 m
(iv)
29.58 m
(v)
34.58 m
Question
15
15.
The angles of depression of two boats from the top of a cliff 80 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
(i)
218.57 m
(ii)
232.57 m
(iii)
193.57 m
(iv)
236.57 m
(v)
205.57 m
Question
16
16.
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 6 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
(i)
7 min 11 sec
(ii)
9 min 13 sec
(iii)
6 min 9 sec
(iv)
8 min 12 sec
(v)
10 min 14 sec
Question
17
17.
The shadow of a vertical tower BA on a level ground is increased by 15 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .
(i)
40.49 m
(ii)
30.49 m
(iii)
35.49 m
(iv)
38.49 m
(v)
32.49 m
Question
18
18.
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 60° and 30° and the distance between them is 250 m , find the height of the cliff.
(i)
95.26 m
(ii)
115.26 m
(iii)
92.26 m
(iv)
108.26 m
(v)
123.26 m
Question
19
19.
A man in a boat rowing away from a lighthouse 65 m high, takes 5 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.
(i)
7.16 m/sec
(ii)
0.16 m/sec
(iii)
2.16 m/sec
(iv)
8.16 m/sec
(v)
1.16 m/sec
Question
20
20.
Two vertical poles are on either side of a road. A 40 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against another pole, it makes an angle of 45° with the road. Find the width of the road.
(i)
45.28 m
(ii)
48.28 m
(iii)
51.28 m
(iv)
43.28 m
(v)
53.28 m
Assignment Key
1) (ii)
2) (ii)
3) (v)
4) (v)
5) (ii)
6) (i)
7) (iv)
8) (iv)
9) (i)
10) (i)
11) (iv)
12) (ii)
13) (iii)
14) (iv)
15) (i)
16) (iv)
17) (iii)
18) (iv)
19) (ii)
20) (ii)
