Question

1.6-metre tall man stands 11 m from the base of a tree. He views the top of the tree at an

angle of elevation of 58°. How tall is the tree?

Answer 1

17.60m

Explanation

The set up is a right angled triangle

Given

angle of elevation = 58°

Distance of the man from the tree = adjacent = 11m

Required

Height of the tree h (Opposite)

Using the TOA identity

tan theta = opposite/adjacent

tan 58 = h/11

h = 11tan58

h = 11(1.6)

h = 17.60

Hence the tree is 17.60m tall