Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 600 . When he moves 40 metres away from the bank, he finds the angle of elevation to be 300 . Find the height of the tree and the width of the river.

Answer 1

The total width of the road is given by

W = w1 + w2

where w1 = l.sin(alpha), and w2 = l.cos(alpha)

and l = 30 m and alpha = 32.4 degrees.

So, w1 = 30*sin(32.4) = 16.075 m, and w2 = 30*cos(32.4) = 25.330 m

Giving W = w1 + w2 = 41.405 m