A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30°

Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Accepted Answer

Let the unbroken part be $h1$ and the broken part be $h2$. Base distance $x = 8$ m. $\cos 30^\circ = \frac{8}{h2} \implies \frac{\sqrt{3}}{2} = \frac{8}{h2} \implies h2 = \frac{16}{\sqrt{3}}$. Also $	an 30^\circ = \frac{h1}{8} \implies \frac{1}{\sqrt{3}} = \frac{h1}{8} \implies h1 = \frac{8}{\sqrt{3}}$. Total height = $h1 + h2 = \frac{8}{\sqrt{3}} + \frac{16}{\sqrt{3}} = \frac{24}{\sqrt{3}} = 8\sqrt{3}$ m.

Applications of Trigonometry

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