# throwback maths 5

Nice bit of trigonometry. (Still an awful tree)

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