EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 50 m, find the height of the building .
(i)
16.67 m
(ii)
19.67 m
(iii)
11.67 m
(iv)
21.67 m
(v)
13.67 m
Question
2
2.
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 45° and 60° respectively. Find the height of the other temple.
(i)
89.53 m
(ii)
84.53 m
(iii)
87.53 m
(iv)
79.53 m
(v)
81.53 m
Question
3
3.
Two poles of equal height are standing opposite to each other on either side of a road which is 35 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 23°33' and 33°35' respectively. Find the height of each pole and the distances of the point from the two poles .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
23
0.4245
0.4265
0.4286
0.4307
0.4327
0.4348
0.4369
0.4390
0.4411
0.4431
3
7
10
14
17
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
33
0.6494
0.6519
0.6544
0.6569
0.6594
0.6619
0.6644
0.6669
0.6694
0.6720
4
8
13
17
21
(i)
height =
7.21 m
, distances away =
11.87 m
,
19.13 m
(ii)
height =
11.21 m
, distances away =
15.87 m
,
23.13 m
(iii)
height =
9.21 m
, distances away =
13.87 m
,
21.13 m
(iv)
height =
10.21 m
, distances away =
14.87 m
,
22.13 m
(v)
height =
8.21 m
, distances away =
12.87 m
,
20.13 m
Question
4
4.
From the top of a 17 m high building , the angle of elevation of the top of a cable tower is 44°11' and the angle of depression of its foot is 26°34'. Find the height of the cable tower.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
44
0.9657
0.9691
0.9725
0.9759
0.9793
0.9827
0.9861
0.9896
0.9930
0.9965
6
11
17
23
28
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
26
0.4877
0.4899
0.4921
0.4942
0.4964
0.4986
0.5008
0.5029
0.5051
0.5073
4
7
11
15
18
(i)
45.04 m
(ii)
47.04 m
(iii)
55.04 m
(iv)
50.04 m
(v)
53.04 m
Question
5
5.
The angles of depression of two boats from the top of a cliff 60 m high are 47° and 43° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
43
0.9325
0.9358
0.9391
0.9424
0.9457
0.9490
0.9523
0.9556
0.9590
0.9623
6
11
17
22
28
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
47
1.0724
1.0761
1.0799
1.0837
1.0875
1.0913
1.0951
1.0990
1.1028
1.1067
6
13
19
25
32
(i)
9.39 m
(ii)
6.39 m
(iii)
8.39 m
(iv)
10.39 m
(v)
7.39 m
Question
6
6.
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 235 m , find the height of the cliff.
(i)
81.02 m
(ii)
89.02 m
(iii)
83.02 m
(iv)
91.02 m
(v)
86.02 m
Question
7
7.
A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
cos
(-1)
(
5
6
)
.
If the distance between the point and the top of the
tower
is
100 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
78.33 m
(ii)
86.33 m
(iii)
80.33 m
(iv)
88.33 m
(v)
83.33 m
Question
8
8.
From the top of a light house which is 95 m high from the sea level, the angles of depression of two ships are 37°41' and 29°11'. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
37
0.7536
0.7563
0.7590
0.7618
0.7646
0.7673
0.7701
0.7729
0.7757
0.7785
5
9
14
19
23
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
29
0.5543
0.5566
0.5589
0.5612
0.5635
0.5658
0.5681
0.5704
0.5727
0.5750
4
8
12
15
19
(i)
52.11 m
(ii)
47.11 m
(iii)
44.11 m
(iv)
50.11 m
(v)
42.11 m
Question
9
9.
A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
60°
.
If the distance between the point and the foot of the
chimney
is
50 m
,
find the height of the
chimney
.
(i)
150
m
(ii)
50
√
3
m
(iii)
75
√
2
m
(iv)
50
√
18
m
(v)
50
m
Question
10
10.
The shadow of a vertical tower BA on a level ground is increased by 10 m, when the altitude of the sun changes from 59° to 34°. Find the height of the tower .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
59
1.6643
1.6709
1.6775
1.6842
1.6909
1.6977
1.7045
1.7113
1.7182
1.7251
11
23
34
45
56
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
34
0.6745
0.6771
0.6796
0.6822
0.6847
0.6873
0.6899
0.6924
0.6930
0.6976
4
9
13
17
22
(i)
11.34 m
(ii)
14.34 m
(iii)
16.34 m
(iv)
8.34 m
(v)
6.34 m
Question
11
11.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 180 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 42°15' and 56°4' respectively. Find the width of the river .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
42
0.9004
0.9036
0.9067
0.9099
0.9131
0.9163
0.9195
0.9228
0.9260
0.9293
5
11
16
21
27
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
56
1.4826
1.4882
1.4938
1.4994
1.5051
1.5108
1.5166
1.5224
1.5282
1.5340
10
19
29
38
48
(i)
121.10 m
(ii)
93.10 m
(iii)
137.10 m
(iv)
139.10 m
(v)
107.10 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 60° and 45° respectively. Find the height of the pillar.
(i)
100.46 m
(ii)
151.46 m
(iii)
137.46 m
(iv)
120.46 m
(v)
124.46 m
Question
13
13.
The angles of depression of two boats from the top of a cliff 190 m high are 35° and 47° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
55
1.4281
1.4335
1.4388
1.4442
1.4496
1.4550
1.4605
1.4659
1.4715
1.4770
9
18
27
36
45
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
43
0.9325
0.9358
0.9391
0.9424
0.9457
0.9490
0.9523
0.9556
0.9590
0.9623
6
11
17
22
28
(i)
436.51 m
(ii)
470.51 m
(iii)
435.51 m
(iv)
465.51 m
(v)
448.51 m
Question
14
14.
A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
30°
.
If the height of the
chimney
is
120 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
240
m
(ii)
237
m
(iii)
239
m
(iv)
243
m
(v)
241
m
Question
15
15.
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 34°39' and 50°36' respectively. Find the height of the other temple.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
34
0.6745
0.6771
0.6796
0.6822
0.6847
0.6873
0.6899
0.6924
0.6930
0.6976
4
9
13
17
22
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
50
1.1918
1.1960
1.2002
1.2045
1.2088
1.2131
1.2174
1.2218
1.2261
1.2305
7
14
22
29
36
(i)
89.45 m
(ii)
91.45 m
(iii)
83.45 m
(iv)
86.45 m
(v)
81.45 m
Question
16
16.
From a point 150 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 60° and 45° respectively. Find the height of the cliff.
(i)
126.00 m
(ii)
163.00 m
(iii)
150.00 m
(iv)
148.00 m
(v)
166.00 m
Question
17
17.
A flagstaff stands on the top of a building at a distance of 15 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 30°. Find the height of the flagstaff .
(i)
10
√
18
m
(ii)
10
√
3
m
(iii)
10
m
(iv)
30
m
(v)
15
√
2
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 20° and 48° and the distance between them is 240 m , find the height of the cliff.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
20
0.3640
0.3659
0.3679
0.3699
0.3719
0.3739
0.3759
0.3779
0.3799
0.3819
3
7
10
13
17
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
48
1.1106
1.1145
1.1184
1.1224
1.1263
1.1303
1.1343
1.1383
1.1423
1.1463
7
13
20
27
33
(i)
70.80 m
(ii)
60.80 m
(iii)
65.80 m
(iv)
62.80 m
(v)
68.80 m
Question
19
19.
The angles of depression of two boats from the top of a cliff 90 m high are 30° and 45° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
(i)
70.89 m
(ii)
65.89 m
(iii)
62.89 m
(iv)
60.89 m
(v)
68.89 m
Question
20
20.
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 60°, how soon after this, will the car reach the observation tower?
(i)
5 min 8 sec
(ii)
4 min 6 sec
(iii)
0 min 3 sec
(iv)
2 min 4 sec
(v)
3 min 0 sec
Question
21
21.
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 32°25'. If the distance between the observation point and the foot of the radio tower is 6 m, find the height of the radio tower.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
32
0.6249
0.6273
0.6297
0.6322
0.6346
0.6371
0.6395
0.6420
0.6445
0.6469
4
8
12
17
21
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
32
0.8480
0.8471
0.8462
0.8453
0.8443
0.8434
0.8425
0.8415
0.8406
0.8393
2
3
5
6
8
(i)
3.81 m
(ii)
4.81 m
(iii)
5.81 m
(iv)
2.81 m
(v)
1.81 m
Question
22
22.
From a point 200 m above a lake, the angle of elevation of a cloud is 30° and the angle of depression of its reflection in the lake is 65°. Find the height of the cloud from the lake.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
30
0.5774
0.5797
0.5820
0.5844
0.5867
0.5890
0.5914
0.5938
0.5961
0.5985
4
8
12
16
20
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
65
2.1445
2.1543
2.1642
2.1742
2.1842
2.1943
2.2045
2.2148
2.2251
2.2355
17
34
51
68
85
(i)
369.38 m
(ii)
347.38 m
(iii)
365.38 m
(iv)
332.38 m
(v)
330.38 m
Question
23
23.
A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
cosec
(-1)
(
11
9
)
.
If the distance between the point and the top of the
tower
is
140 m
,
find the height of the
tower
.
(i)
114.55 m
(ii)
129.55 m
(iii)
102.55 m
(iv)
87.55 m
(v)
126.55 m
Question
24
24.
A man in a boat rowing away from a lighthouse 30 m high, takes 4 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
(i)
1.05 m/sec
(ii)
8.05 m/sec
(iii)
2.05 m/sec
(iv)
0.05 m/sec
(v)
7.05 m/sec
Question
25
25.
The shadow of a vertical tower BA on a level ground is increased by 50 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .
(i)
114.30 m
(ii)
118.30 m
(iii)
96.30 m
(iv)
131.30 m
(v)
134.30 m
Assignment Key
1) (i)
2) (ii)
3) (iii)
4) (iv)
5) (iii)
6) (v)
7) (v)
8) (ii)
9) (ii)
10) (i)
11) (i)
12) (v)
13) (v)
14) (i)
15) (iv)
16) (iii)
17) (ii)
18) (iii)
19) (ii)
20) (v)
21) (i)
22) (ii)
23) (i)
24) (iv)
25) (ii)
