Question

Q1 [5]

A cliff is located on the edge of a river. An observation tower, 11 meters tall, is built on the
cliff. The angle between the top of the cliff and the opposite side of the river is 20°, while the angle
between the top of the tower and the opposite side of the river is 30° Let's define h as the height of
the cliff and w the width of the river.
iii. Draw the cliff, tower and river writing all the information given (1pt)
Find the width of the river (4 pt)
iv.

Answer 1

The required drawing showing the cliff, river, and tower as well as the details in the question is attached, please find alongside the answer

The width of the river is approximately 51.55 meters

Explanation:

The height of the observation tower = 11 meters

The angle of elevation of the cliff top and the opposite side of the river = 20°

The angle of elevation of the tower top and the opposite side of the river = 30°

Therefore, by sine rule, we have;

h/sin(20) = w/sin(60)

11/sin(10) = length, l/sin(60)

l = sin(60) ×11/sin(10) ≈ 54.86 meters

w = l × cos (20) = 54.86 meters × cos (20) ≈ 51.55 meters

The width, w, of the river is approximately 51.55 meters.