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

let the height of tree be h

width of river be x

$tan60 = \sqrt{3} = \frac{h}{x} \\ h = \sqrt{3} x \: \: \\ tan30 = \frac{1}{ \sqrt{3} } = \frac{h}{x + 40} \\ h = \frac{x + 40}{ \sqrt{3} } \\ \sqrt{3}x = \frac{x + 40}{ \sqrt{3} } \\ \sqrt{3} \times \sqrt{3} \times x = x + 40 \\ 3x = x + 40 \\ 2x = 40 \\ x = 20 \\ h = 20 \times \sqrt{3} \\ h = 20 \sqrt{3}$

Answer 2

$\textbf{Answer is in Attachment !}$