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  • A tree is broken due to wind and broken part touches to ground at an angle of 30°. If distance between top and foot of tree is 8m. Find height of tree.

A tree is broken due to wind and broken part touches to ground at an angle of 30°. If distance between top and foot of tree is 8m. Find height of tree.

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$ Assume the original height of the tree was H and after broken it has height h $ \\ $ Distance between top and foot of tree is (b) $ = 8m\\ \tan 30 = \frac{h}{8} \\ \frac{1}{\sqrt{3}} = \frac{h}{8} \\ h = \frac{8}{\sqrt{3}} \\ \sin 30 = \frac{h}{H-h} \\ \frac{1}{2} = \frac{h}{H-h} \\ \frac{H-h}{h} = 2 \\ \frac{H}{h} = 3 \\ H = 3h = 3 \times \frac{8}{\sqrt{3}} \\ $ Height of the tree (H) = $ 8 \sqrt{3} \\

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Ravindra Pindel

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