EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Two vertical poles are on either side of a road. A 34 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 25°31' with the pole and when it is turned to rest against another pole, it makes an angle of 32°58' with the road. Find the width of the road.
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
25
0.9063
0.9056
0.9048
0.9041
0.9033
0.9026
0.9018
0.9011
0.9003
0.8996
1
3
4
5
7
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)
64.20 m
(ii)
59.20 m
(iii)
56.20 m
(iv)
62.20 m
(v)
54.20 m
Question
2
2.
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 flag staff is 8 m, find the height of the building .
(i)
7.93 m
(ii)
15.93 m
(iii)
5.93 m
(iv)
10.93 m
(v)
13.93 m
Question
3
3.
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 49°11'. If the distance between the observation point and the foot of the chimney is 2 m, find the distance between the observation point and the top of the chimney.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
49
1.1504
1.1544
1.1585
1.1626
1.1667
1.1708
1.1750
1.1792
1.1833
1.1875
7
14
21
27
34
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
49
0.6561
0.6547
0.6534
0.6521
0.6508
0.6494
0.6481
0.6468
0.6455
0.6441
2
4
7
9
11
(i)
5.06 m
(ii)
1.06 m
(iii)
4.06 m
(iv)
3.06 m
(v)
2.06 m
Question
4
4.
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
30 m
,
find the distance between
the observation point and the top of the
building
.
(i)
60
m
(ii)
63
m
(iii)
59
m
(iv)
57
m
(v)
61
m
Question
5
5.
A man in a boat rowing away from a lighthouse 90 m high, takes 1.5 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
(i)
0.42 m/sec
(ii)
1.42 m/sec
(iii)
8.42 m/sec
(iv)
7.42 m/sec
(v)
2.42 m/sec
Question
6
6.
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 33°36'. If the distance between the observation point and the foot of the tower is 12 m, 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'
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
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
33
0.8387
0.8377
0.8368
0.8358
0.8348
0.8339
0.8329
0.8320
0.8310
0.8300
2
3
5
7
8
(i)
8.97 m
(ii)
5.97 m
(iii)
7.97 m
(iv)
6.97 m
(v)
9.97 m
Question
7
7.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 70 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 44°41' and 58°1' 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'
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'
58
1.6003
1.6066
1.6128
1.6191
1.6255
1.6319
1.6383
1.6447
1.6512
1.6577
11
21
32
43
53
(i)
23.77 m
(ii)
31.77 m
(iii)
26.77 m
(iv)
29.77 m
(v)
21.77 m
Question
8
8.
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
tan
(-1)
(
7
8
)
.
If the distance between the point and the foot of the
tower
is
90 m
,
find the height of the
tower
.
(i)
78.75 m
(ii)
81.75 m
(iii)
73.75 m
(iv)
83.75 m
(v)
75.75 m
Question
9
9.
From the top of a 11 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)
49.00 m
(ii)
39.00 m
(iii)
44.00 m
(iv)
47.00 m
(v)
41.00 m
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
60°
.
If the distance between the point and the top of the
radio tower
is
20 m
,
find the height of the
radio tower
.
(i)
15
√
2
m
(ii)
10
√
3
m
(iii)
10
m
(iv)
30
m
(v)
10
√
18
m
Question
11
11.
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 ?
(i)
∠c
(ii)
∠e
(iii)
∠d
(iv)
∠b
Question
12
12.
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 15 min for the angle of depression to change from 23° to 46°, how soon after this, will the car reach the observation tower?
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'
46
1.0355
1.0392
1.0428
1.0464
1.0501
1.0538
1.0575
1.0612
1.0649
1.0686
6
12
18
25
31
(i)
9 min 24 sec
(ii)
12 min 27 sec
(iii)
10 min 25 sec
(iv)
8 min 23 sec
(v)
11 min 26 sec
Question
13
13.
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 28° and 43° and the distance between them is 185 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'
28
0.5317
0.5340
0.5362
0.5384
0.5407
0.5430
0.5452
0.5475
0.5498
0.5520
4
8
11
15
19
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)
67.65 m
(ii)
62.65 m
(iii)
59.65 m
(iv)
57.65 m
(v)
65.65 m
Question
14
14.
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 17 m, find the height of the flag staff .
(i)
15.45 m
(ii)
9.45 m
(iii)
17.45 m
(iv)
12.45 m
(v)
7.45 m
Question
15
15.
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 140 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
496.49 m
(ii)
534.49 m
(iii)
522.49 m
(iv)
545.49 m
(v)
505.49 m
Question
16
16.
From a point 130 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 30° respectively. Find the height of the cliff.
(i)
70.06 m
(ii)
72.06 m
(iii)
80.06 m
(iv)
75.06 m
(v)
78.06 m
Question
17
17.
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 47°6' and the angle of elevation of the top of the building is 33°28'. If the height of the flag staff is 16 m, find the height of the building .
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
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)
22.49 m
(ii)
25.49 m
(iii)
30.49 m
(iv)
28.49 m
(v)
20.49 m
Question
18
18.
Two poles of equal height are standing opposite to each other on either side of a road which is 45 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 45° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .
(i)
height =
17.47 m
, distances away =
29.53 m
,
17.47 m
(ii)
height =
18.47 m
, distances away =
30.53 m
,
18.47 m
(iii)
height =
16.47 m
, distances away =
28.53 m
,
16.47 m
(iv)
height =
15.47 m
, distances away =
27.53 m
,
15.47 m
(v)
height =
14.47 m
, distances away =
26.53 m
,
14.47 m
Question
19
19.
A flagstaff stands on the top of a building at a distance of 10 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)
200
m
(ii)
(
2
−
√
3
)
m
(iii)
(
15
√
2
−
5
√
6
)
m
(iv)
(
10
√
18
−
10
√
6
)
m
(v)
(
10
√
3
−
10
)
m
Question
20
20.
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
cot
(-1)
(
1
5
)
.
If the height of the
tower
is
20 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
2.00 m
(ii)
5.00 m
(iii)
6.00 m
(iv)
3.00 m
(v)
4.00 m
Question
21
21.
The shadow of a vertical tower BA on a level ground is increased by 25 m, when the altitude of the sun changes from 50° to 29°. 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'
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
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)
25.91 m
(ii)
30.91 m
(iii)
20.91 m
(iv)
22.91 m
(v)
28.91 m
Question
22
22.
The angles of depression of two boats from the top of a cliff 130 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
(i)
136.11 m
(ii)
150.11 m
(iii)
135.11 m
(iv)
152.11 m
(v)
167.11 m
Question
23
23.
Two poles of equal height are standing opposite to each other on either side of a road which is 30 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 36°59' and 29°4' 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'
36
0.7265
0.7292
0.7319
0.7346
0.7373
0.7400
0.7427
0.7454
0.7481
0.7508
5
9
14
18
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)
height =
9.59 m
, distances away =
17.26 m
,
12.74 m
(ii)
height =
7.59 m
, distances away =
15.26 m
,
10.74 m
(iii)
height =
8.59 m
, distances away =
16.26 m
,
11.74 m
(iv)
height =
11.59 m
, distances away =
19.26 m
,
14.74 m
(v)
height =
10.59 m
, distances away =
18.26 m
,
13.74 m
Question
24
24.
From a point 90 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°44' and 20°20' respectively. 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'
45
1.0000
1.0035
1.0070
1.0105
1.0141
1.0176
1.0212
1.0247
1.0283
1.0319
6
12
18
24
30
(i)
38.35 m
(ii)
36.35 m
(iii)
28.35 m
(iv)
30.35 m
(v)
33.35 m
Question
25
25.
A pole stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the pole is found to be 43°57'. If the distance between the observation point and the top of the pole is 20 m, find the distance between the observation point and the foot of the pole.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
43
0.6820
0.6833
0.6845
0.6858
0.6871
0.6884
0.6896
0.6909
0.6921
0.6934
2
4
6
9
11
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
43
0.7314
0.7302
0.7290
0.7278
0.7266
0.7254
0.7242
0.7230
0.7218
0.7206
2
4
6
8
10
(i)
14.40 m
(ii)
19.40 m
(iii)
9.40 m
(iv)
17.40 m
(v)
11.40 m
Assignment Key
1) (ii)
2) (iv)
3) (iv)
4) (i)
5) (i)
6) (iii)
7) (iii)
8) (i)
9) (iii)
10) (ii)
11) (iv)
12) (iii)
13) (ii)
14) (iv)
15) (iii)
16) (iv)
17) (ii)
18) (iii)
19) (v)
20) (v)
21) (i)
22) (ii)
23) (i)
24) (v)
25) (i)
