EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
From the top of a 16 m high building , the angle of elevation of the top of a cable tower is 45° and the angle of depression of its foot is 30°. Find the height of the cable tower.
(i)
46.71 m
(ii)
38.71 m
(iii)
40.71 m
(iv)
48.71 m
(v)
43.71 m
Question
2
2.
From the top of a light house which is 45 m high from the sea level, the angles of depression of two ships are 33°12' and 20°53'. 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'
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'
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
(i)
54.16 m
(ii)
46.16 m
(iii)
49.16 m
(iv)
44.16 m
(v)
52.16 m
Question
3
3.
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 25°37' and the angle of elevation of the top of the building is 20°2'. If the height of the building is 15 m, find the height of the flag staff .
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'
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)
3.72 m
(ii)
6.72 m
(iii)
4.72 m
(iv)
5.72 m
(v)
2.72 m
Question
4
4.
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)
(
1
4
)
.
If the distance between the point and the foot of the
tower
is
200 m
,
find the height of the
tower
.
(i)
47.00 m
(ii)
50.00 m
(iii)
53.00 m
(iv)
55.00 m
(v)
45.00 m
Question
5
5.
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
30°
.
If the distance between the point and the foot of the
building
is
170 m
,
find the distance between
the observation point and the top of the
building
.
(i)
340
3
√
3
m
(ii)
340
m
(iii)
170
√
2
m
(iv)
340
3
m
(v)
340
3
√
18
m
Question
6
6.
The angles of depression of two boats from the top of a cliff 50 m high are 28° and 26° 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'
62
1.8807
1.8887
1.8967
1.9047
1.9128
1.9210
1.9292
1.9375
1.9458
1.9542
14
27
41
55
68
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)
6.48 m
(ii)
10.48 m
(iii)
8.48 m
(iv)
7.48 m
(v)
9.48 m
Question
7
7.
From a point 100 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)
114.00 m
(ii)
85.00 m
(iii)
100.00 m
(iv)
88.00 m
(v)
128.00 m
Question
8
8.
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 51°9'. If the distance between the observation point and the top of the pole is 6 m, find the height of the pole.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
51
0.7771
0.7782
0.7793
0.7804
0.7815
0.7826
0.7837
0.7848
0.7859
0.7869
2
4
5
7
9
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
51
0.6293
0.6280
0.6266
0.6252
0.6239
0.6225
0.6211
0.6198
0.6184
0.9170
2
5
7
9
12
(i)
5.67 m
(ii)
4.67 m
(iii)
3.67 m
(iv)
6.67 m
(v)
2.67 m
Question
9
9.
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 pillar.
(i)
66.84 m
(ii)
74.84 m
(iii)
71.84 m
(iv)
76.84 m
(v)
68.84 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 30°13'. If the distance between the observation point and the foot of the radio tower is 17 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'
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 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)
7.90 m
(ii)
9.90 m
(iii)
11.90 m
(iv)
8.90 m
(v)
10.90 m
Question
11
11.
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 57°24'. If the height of the tower is 6 m, find the distance between the observation point and the foot of the tower.
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
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
57
0.8387
0.8396
0.8406
0.8415
0.8425
0.8434
0.8443
0.8453
0.8462
0.8471
2
3
5
6
8
(i)
3.84 m
(ii)
2.84 m
(iii)
1.84 m
(iv)
5.84 m
(v)
4.84 m
Question
12
12.
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 190 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
727.10 m
(ii)
709.10 m
(iii)
685.10 m
(iv)
704.10 m
(v)
716.10 m
Question
13
13.
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
30°
.
If the distance between the point and the top of the
radio tower
is
60 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
45
√
2
m
(ii)
90
m
(iii)
30
√
18
m
(iv)
30
m
(v)
30
√
3
m
Question
14
14.
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 21°10' and 49°59' 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'
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'
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
(i)
height =
12.23 m
, distances away =
10.59 m
,
28.41 m
(ii)
height =
8.23 m
, distances away =
6.59 m
,
24.41 m
(iii)
height =
9.23 m
, distances away =
7.59 m
,
25.41 m
(iv)
height =
11.23 m
, distances away =
9.59 m
,
27.41 m
(v)
height =
10.23 m
, distances away =
8.59 m
,
26.41 m
Question
15
15.
A man 1.7 m tall stands at a distance of 6.8 m from a lamp post and casts a shadow of 4.9 m on the ground. Find the height of the lamp post .
(i)
5.06 m
(ii)
4.06 m
(iii)
6.06 m
(iv)
3.06 m
(v)
2.06 m
Question
16
16.
An observer 1.8 m tall, is 160 m away from a tower . The angle of elevation of the top of the tower from her eyes is 45°. Find the height of the tower .
(i)
187.80 m
(ii)
133.80 m
(iii)
178.80 m
(iv)
161.80 m
(v)
148.80 m
Question
17
17.
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 41°9'. If the distance between the observation point and the top of the building is 13 m, find the distance between the observation point and the foot of the building.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
41
0.6561
0.6574
0.6587
0.6600
0.6613
0.6626
0.6639
0.6652
0.6665
0.6678
2
4
7
9
11
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
41
0.7547
0.7536
0.7524
0.7513
0.7501
0.7490
0.7478
0.7466
0.7455
0.7443
2
4
6
8
10
(i)
7.79 m
(ii)
11.79 m
(iii)
9.79 m
(iv)
8.79 m
(v)
10.79 m
Question
18
18.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 140 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°54' and 69°9' 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'
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'
69
2.6051
2.6187
2.6325
2.6464
2.6605
2.6746
2.6889
2.7034
2.7179
2.7326
24
47
71
95
119
(i)
53.32 m
(ii)
48.32 m
(iii)
56.32 m
(iv)
58.32 m
(v)
50.32 m
Question
19
19.
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 41°38' and the angle of elevation of the top of the building is 29°6'. If the height of the flag staff is 14 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'
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)
18.46 m
(ii)
23.46 m
(iii)
28.46 m
(iv)
20.46 m
(v)
26.46 m
Question
20
20.
At the foot of a mountain, the elevation of its summit is 50°. After ascending 1000 m towards the mountain up an incline of 28°, the elevation changes to 65°. Find the height of the mountain.
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'
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
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
28
0.8829
0.8821
0.8813
0.8805
0.8796
0.8788
0.8780
0.8771
0.8763
0.8755
1
3
4
5
7
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
28
0.4695
0.4710
0.4726
0.4741
0.4756
0.4772
0.4787
0.4802
0.4818
0.4833
3
5
9
10
13
(i)
1631.07 m
(ii)
1961.07 m
(iii)
1701.07 m
(iv)
1781.07 m
(v)
2011.07 m
Question
21
21.
Two boys are on opposite sides of a tower of 20 m height. They measure the angle of elevation of the top of the tower as 45° and 30° respectively. Find the distance between the two boys.
(i)
(
10
√
6
+
30
√
2
)
m
(ii)
(
20
√
6
+
20
√
18
)
m
(iii)
(
−
2
−
√
3
)
m
(iv)
(
20
+
20
√
3
)
m
(v)
(
−
800
)
m
Question
22
22.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 32°53' with the ground. The top of the tree touches the ground at a distance of 190 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'
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)
361.10 m
(ii)
336.10 m
(iii)
349.10 m
(iv)
366.10 m
(v)
335.10 m
Question
23
23.
A man in a boat rowing away from a lighthouse 70 m high, takes 1 min to change the angle of elevation of the top of the lighthouse from 32° to 25°. Find the speed of the boat.
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
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
(i)
0.64 m/sec
(ii)
7.64 m/sec
(iii)
2.64 m/sec
(iv)
8.64 m/sec
(v)
1.64 m/sec
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
cos
(-1)
(
1
3
)
.
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)
28.33 m
(ii)
33.33 m
(iii)
30.33 m
(iv)
38.33 m
(v)
36.33 m
Question
25
25.
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
3
)
.
If the height of the
tower
is
90 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
30.00 m
(ii)
27.00 m
(iii)
35.00 m
(iv)
25.00 m
(v)
33.00 m
Assignment Key
1) (v)
2) (iii)
3) (iii)
4) (ii)
5) (i)
6) (iii)
7) (iii)
8) (ii)
9) (iii)
10) (ii)
11) (i)
12) (ii)
13) (v)
14) (v)
15) (ii)
16) (iv)
17) (iii)
18) (i)
19) (ii)
20) (iv)
21) (iv)
22) (iii)
23) (i)
24) (ii)
25) (i)
