Question

In Fig. 17.20, from a boat 200 m away from a vertical
a vertical concrete pillar at the edge of the cliff are
cliff'the angles of elevation of the top and the foot of
21° and 18°30'. Calculate:
(1) the height of the cliff;
(ii) the height of the pillar.
[Hint. Use tables to find tan 21° and tan 18°30'.]
Pillar
21°
Cliff
18°30
Boat
200 m​

Answer 1

Given :

Distance of boat from a vertical concrete pillar = 200m

Angle of elevation of the top and the foot = 21° and 18°30'

To find :

i) The height of the cliff

ii) The height of the pillar

Solution :

i) Let the height of the cliff = h

tan 18°30' = h / 200

0.33 = h / 200

h = 0.33 × 200

h = 66m

The height of the cliff = 66m

ii) Let the height of the pillar = x

tan 21° = (x + 66) / 200

0.38 = (x + 66) / 200

x + 66 = 0.38 × 200

x + 66 = 76

x = 10m

The height of the pillar = 10m

Therefore, The height of the cliff = 66m and The height of the pillar = 10m