EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 40 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)
21.91 m
(ii)
16.91 m
(iii)
13.91 m
(iv)
11.91 m
(v)
19.91 m
Question
2
2.
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 55°49'. If the height of the pole is 4 m, find the distance between the observation point and the top of the pole.
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 Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
55
0.8192
0.8202
0.8211
0.8221
0.8231
0.8241
0.8251
0.8261
0.8271
0.8281
2
3
5
7
8
(i)
5.84 m
(ii)
4.84 m
(iii)
3.84 m
(iv)
6.84 m
(v)
2.84 m
Question
3
3.
From a point 70 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)
37.42 m
(ii)
35.42 m
(iii)
43.42 m
(iv)
45.42 m
(v)
40.42 m
Question
4
4.
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 33°42' and the angle of elevation of the top of the building is 29°38'. If the height of the flag staff is 11 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'
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
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)
68.86 m
(ii)
58.86 m
(iii)
66.86 m
(iv)
63.86 m
(v)
60.86 m
Question
5
5.
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 60°. If the height of the tower is 50 m, find the height of the building .
(i)
25.87 m
(ii)
31.87 m
(iii)
28.87 m
(iv)
23.87 m
(v)
33.87 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 90 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 50°25' and 64°39' 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'
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'
64
2.0503
2.0594
2.0686
2.0778
2.0872
2.0965
2.1060
2.1155
2.1251
2.1348
16
31
47
63
78
(i)
41.43 m
(ii)
43.43 m
(iii)
38.43 m
(iv)
35.43 m
(v)
33.43 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
30°
.
If the distance between the point and the foot of the
tower
is
90 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
180
m
(ii)
60
√
3
m
(iii)
90
√
2
m
(iv)
60
m
(v)
60
√
18
m
Question
8
8.
The shadow of a vertical tower BA on a level ground is increased by 15 m, when the altitude of the sun changes from 52° to 39°. 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'
52
1.2799
1.2846
1.2892
1.2938
1.2985
1.3032
1.3079
1.3127
1.3175
1.3222
8
16
24
31
39
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
39
0.8098
0.8127
0.8156
0.8185
0.8214
0.8243
0.8273
0.8302
0.8332
0.8361
5
10
15
19
24
(i)
30.07 m
(ii)
38.07 m
(iii)
36.07 m
(iv)
33.07 m
(v)
28.07 m
Question
9
9.
The angles of depression of two boats from the top of a cliff 80 m high are 31° and 33° 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'
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'
57
1.5399
1.5458
1.5517
1.5577
1.5637
1.5697
1.5757
1.5818
1.5880
1.5941
10
20
30
40
50
(i)
10.95 m
(ii)
7.95 m
(iii)
9.95 m
(iv)
8.95 m
(v)
11.95 m
Question
10
10.
A man in a boat rowing away from a lighthouse 35 m high, takes 3.5 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.
(i)
7.19 m/sec
(ii)
2.19 m/sec
(iii)
0.19 m/sec
(iv)
8.19 m/sec
(v)
1.19 m/sec
Question
11
11.
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 48°51'. If the distance between the observation point and the top of the pole is 12 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'
48
0.7431
0.7443
0.7455
0.7466
0.7478
0.7490
0.7501
0.7513
0.7524
0.7536
2
4
6
8
10
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
48
0.6691
0.6678
0.6665
0.6652
0.6639
0.6626
0.6613
0.6600
0.6587
0.6574
2
4
7
9
11
(i)
5.90 m
(ii)
7.90 m
(iii)
6.90 m
(iv)
9.90 m
(v)
8.90 m
Question
12
12.
The angle of elevation of the top of a building from the foot of a tower is 20°27'. The angle of elevation of the top of the tower from the foot of the building is 24°46'. If the height of the tower is 100 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'
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'
24
0.4452
0.4473
0.4494
0.4515
0.4536
0.4557
0.4578
0.4599
0.4621
0.4642
4
7
11
14
18
(i)
85.84 m
(ii)
80.84 m
(iii)
83.84 m
(iv)
77.84 m
(v)
75.84 m
Question
13
13.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 49°10' with the ground. The top of the tree touches the ground at a distance of 150 m from the foot of the tree . Find the height of the tree before it was broken.
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)
376.99 m
(ii)
430.99 m
(iii)
402.99 m
(iv)
396.99 m
(v)
417.99 m
Question
14
14.
The shadow of a vertical tower BA on a level ground is increased by 20 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .
(i)
17.32 m
(ii)
22.32 m
(iii)
20.32 m
(iv)
14.32 m
(v)
12.32 m
Question
15
15.
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 38°17' and 24°17' 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'
38
0.7813
0.7841
0.7869
0.7898
0.7926
0.7954
0.7983
0.8012
0.8040
0.8069
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'
24
0.4452
0.4473
0.4494
0.4515
0.4536
0.4557
0.4578
0.4599
0.4621
0.4642
4
7
11
14
18
(i)
height =
9.05 m
, distances away =
21.27 m
,
11.73 m
(ii)
height =
12.05 m
, distances away =
24.27 m
,
14.73 m
(iii)
height =
11.05 m
, distances away =
23.27 m
,
13.73 m
(iv)
height =
8.05 m
, distances away =
20.27 m
,
10.73 m
(v)
height =
10.05 m
, distances away =
22.27 m
,
12.73 m
Question
16
16.
From a point 120 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)
45.71 m
(ii)
53.71 m
(iii)
55.71 m
(iv)
50.71 m
(v)
47.71 m
Question
17
17.
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
sec
(-1)
(
5
3
)
.
If the distance between the point and the top of the
tower
is
70 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
42.00 m
(ii)
47.00 m
(iii)
39.00 m
(iv)
37.00 m
(v)
45.00 m
Question
18
18.
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 11 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?
(i)
2 min 27 sec
(ii)
4 min 29 sec
(iii)
7 min 32 sec
(iv)
6 min 31 sec
(v)
5 min 30 sec
Question
19
19.
An observer 1.6 m tall, is 120 m away from a tower . The angle of elevation of the top of the tower from her eyes is 37°40'. 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'
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
(i)
99.24 m
(ii)
94.24 m
(iii)
97.24 m
(iv)
91.24 m
(v)
89.24 m
Question
20
20.
From a point 140 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 25°16' and 21°54' 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'
21
0.3839
0.3859
0.3879
0.3899
0.3919
0.3939
0.3959
0.3979
0.4000
0.4020
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'
25
0.4663
0.4684
0.4706
0.4727
0.4748
0.4770
0.4791
0.4813
0.4834
0.4856
4
7
11
14
18
(i)
59.28 m
(ii)
51.28 m
(iii)
61.28 m
(iv)
53.28 m
(v)
56.28 m
Question
21
21.
From the top of a light house which is 25 m high from the sea level, the angles of depression of two ships are 47°59' and 41°23'. 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'
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
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
41
0.8693
0.8724
0.8754
0.8785
0.8816
0.8847
0.8878
0.8910
0.8941
0.8972
5
10
16
21
26
(i)
6.85 m
(ii)
7.85 m
(iii)
4.85 m
(iv)
3.85 m
(v)
5.85 m
Question
22
22.
An aeroplane is flying horizontally 1500 m above the ground. From a point of observation, which lies exactly below the path of the aeroplane, the angle of elevation at a certain instant is 58°. After 30 sec , its elevation from the same point changes to 38°. Find the uniform speed of the aeroplane .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
38
0.7813
0.7841
0.7869
0.7898
0.7926
0.7954
0.7983
0.8012
0.8040
0.8069
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'
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)
102.91 kmph
(ii)
117.91 kmph
(iii)
100.91 kmph
(iv)
129.91 kmph
(v)
133.91 kmph
Question
23
23.
From a point 80 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°18' and 29°32' respectively. Find the height of the pillar.
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
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)
38.51 m
(ii)
30.51 m
(iii)
40.51 m
(iv)
32.51 m
(v)
35.51 m
Question
24
24.
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 30°14'. If the distance between the observation point and the top of the tower is 20 m, find the height of the tower.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
30
0.5000
0.5015
0.5030
0.5045
0.5060
0.5075
0.5090
0.5105
0.5120
0.5135
3
5
8
10
13
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
30
0.8660
0.8652
0.8643
0.8634
0.8625
0.8616
0.8607
0.8599
0.8590
0.8581
1
3
4
6
7
(i)
15.07 m
(ii)
13.07 m
(iii)
5.07 m
(iv)
10.07 m
(v)
7.07 m
Question
25
25.
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 5 m, find the height of the building .
(i)
0.50 m
(ii)
2.50 m
(iii)
4.50 m
(iv)
3.50 m
(v)
1.50 m
Assignment Key
1) (ii)
2) (ii)
3) (v)
4) (iv)
5) (iii)
6) (iii)
7) (ii)
8) (iv)
9) (iii)
10) (iii)
11) (ii)
12) (ii)
13) (iii)
14) (i)
15) (v)
16) (iv)
17) (i)
18) (v)
19) (ii)
20) (v)
21) (v)
22) (ii)
23) (v)
24) (iv)
25) (ii)
