throwback maths 5

Nice bit of trigonometry. (Still an awful tree)

throwback 5
Solution

Let the height of the tree be $h$, let $x$ be the unknown distance between the base of the tree and the closest observation point. Then, the following are true: $$\begin{align} h &= (10+x)\tan(40)\\ h &= x\tan(60) \end{align} $$

This yields $$ h = \frac{10\tan(40)\tan(60)}{\tan(60) - \tan(40)} = 16.28m $$