EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
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 60° and the distance between them is 115 m , find the height of the cliff.
(i)
54.80 m
(ii)
52.80 m
(iii)
46.80 m
(iv)
49.80 m
(v)
44.80 m
Question
2
2.
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 35° and 47° and the distance between them is 225 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'
35
0.7002
0.7028
0.7054
0.7080
0.7107
0.7133
0.7159
0.7186
0.7212
0.7239
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'
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)
92.31 m
(ii)
100.31 m
(iii)
90.31 m
(iv)
98.31 m
(v)
95.31 m
Question
3
3.
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 21°17' and 20°44' 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'
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
(i)
40.86 m
(ii)
42.86 m
(iii)
34.86 m
(iv)
32.86 m
(v)
37.86 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
2
)
.
If the height of the
tower
is
110 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
237.00 m
(ii)
228.00 m
(iii)
214.00 m
(iv)
195.00 m
(v)
220.00 m
Question
5
5.
A man 1.6 m tall stands at a distance of 9.2 m from a lamp post and casts a shadow of 2.7 m on the ground. Find the height of the lamp post .
(i)
9.05 m
(ii)
6.05 m
(iii)
8.05 m
(iv)
7.05 m
(v)
5.05 m
Question
6
6.
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
45°
.
If the height of the
chimney
is
170 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
170
m
(ii)
340
m
(iii)
170
√
2
m
(iv)
85
√
12
m
(v)
340
√
3
m
Question
7
7.
A man in a boat rowing away from a lighthouse 45 m high, takes 1.5 min to change the angle of elevation of the top of the lighthouse from 48° to 38°. 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'
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'
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)
8.19 m/sec
(ii)
0.19 m/sec
(iii)
7.19 m/sec
(iv)
2.19 m/sec
(v)
1.19 m/sec
Question
8
8.
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)
∠f
Question
9
9.
The angles of depression of two boats from the top of a cliff 180 m high are 26° and 39° 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'
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
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
51
1.2349
1.2393
1.2437
1.2484
1.2527
1.2572
1.2617
1.2662
1.2708
1.2753
8
15
23
30
38
(i)
607.34 m
(ii)
591.34 m
(iii)
575.34 m
(iv)
569.34 m
(v)
608.34 m
Question
10
10.
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
45°
.
If the distance between the point and the top of the
tower
is
60 m
,
find the height of the
tower
.
(i)
30
√
2
m
(ii)
15
√
12
m
(iii)
30
m
(iv)
60
m
(v)
60
√
3
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 60 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 60° respectively. Find the height of the other temple.
(i)
37.00 m
(ii)
35.00 m
(iii)
45.00 m
(iv)
43.00 m
(v)
40.00 m
Question
12
12.
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
45°
.
If the height of the
radio tower
is
40 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
43
m
(ii)
40
m
(iii)
38
m
(iv)
39
m
(v)
41
m
Question
13
13.
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 7 m, find the height of the flag staff .
(i)
4.12 m
(ii)
3.12 m
(iii)
5.12 m
(iv)
7.12 m
(v)
6.12 m
Question
14
14.
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 16 min for the angle of depression to change from 32° to 33°, 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'
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 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)
407 min 10 sec
(ii)
411 min 13 sec
(iii)
408 min 6 sec
(iv)
405 min 9 sec
(v)
409 min 12 sec
Question
15
15.
From a point 50 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 pillar.
(i)
60.73 m
(ii)
62.73 m
(iii)
54.73 m
(iv)
57.73 m
(v)
52.73 m
Question
16
16.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?
(i)
∠d
(ii)
∠c
(iii)
∠e
(iv)
∠b
Question
17
17.
At the foot of a mountain, the elevation of its summit is 40°. After ascending 800 m towards the mountain up an incline of 25°, 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'
40
0.8391
0.8421
0.8451
0.8481
0.8511
0.8541
0.8571
0.8601
0.8632
0.8662
5
10
15
20
25
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'
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 Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
25
0.4226
0.4242
0.4258
0.4274
0.4289
0.4305
0.4321
0.4337
0.4352
0.4368
3
5
8
11
13
(i)
798.08 m
(ii)
782.08 m
(iii)
799.08 m
(iv)
759.08 m
(v)
766.08 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 190 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 60° respectively. Find the width of the river .
(i)
109.69 m
(ii)
121.69 m
(iii)
94.69 m
(iv)
102.69 m
Question
19
19.
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 37°6'. If the distance between the observation point and the foot of the building is 8 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'
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 Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
37
0.7986
0.7976
0.7963
0.7955
0.7944
0.7934
0.7923
0.7912
0.7902
0.7891
2
4
5
7
9
(i)
7.05 m
(ii)
5.05 m
(iii)
4.05 m
(iv)
6.05 m
(v)
8.05 m
Question
20
20.
From the top of a light house which is 35 m high from the sea level, the angles of depression of two ships are 60° and 45°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
(i)
14.79 m
(ii)
17.79 m
(iii)
9.79 m
(iv)
11.79 m
(v)
19.79 m
Question
21
21.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60°18' with the ground. The top of the tree touches the ground at a distance of 30 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'
60
1.7321
1.7391
1.7461
1.7532
1.7603
1.7675
1.7747
1.7820
1.7893
1.7966
12
24
36
48
60
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
60
0.5000
0.4985
0.4970
0.4955
0.4939
0.4924
0.4909
0.4894
0.4879
0.4863
3
5
8
10
13
(i)
141.14 m
(ii)
113.14 m
(iii)
105.14 m
(iv)
100.14 m
(v)
127.14 m
Question
22
22.
The angles of depression of two boats from the top of a cliff 160 m high are 49° and 48° 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'
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
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
(i)
2.98 m
(ii)
6.98 m
(iii)
4.98 m
(iv)
5.98 m
(v)
3.98 m
Question
23
23.
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 19 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?
(i)
8 min 29 sec
(ii)
6 min 28 sec
(iii)
12 min 33 sec
(iv)
10 min 31 sec
(v)
9 min 30 sec
Question
24
24.
From the top of a 20 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 45°. Find the height of the cable tower.
(i)
51.64 m
(ii)
49.64 m
(iii)
54.64 m
(iv)
57.64 m
(v)
59.64 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
cos
(-1)
(
1
3
)
.
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)
288.00 m
(ii)
264.00 m
(iii)
248.00 m
(iv)
283.00 m
(v)
270.00 m
Assignment Key
1) (iv)
2) (v)
3) (v)
4) (v)
5) (iv)
6) (iii)
7) (ii)
8) (i)
9) (ii)
10) (i)
11) (v)
12) (ii)
13) (iii)
14) (iii)
15) (iv)
16) (i)
17) (ii)
18) (i)
19) (iv)
20) (i)
21) (ii)
22) (iii)
23) (v)
24) (iii)
25) (v)
