A tree 3

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

Final Answer:

h =  13.8564 m

Step-by-step explanation:

$$\begin{gathered} x=8\text{m} \\ \alpha =30{}^{\circ } \\ \tan \alpha =y:x \\ y=x\cdot \tan \alpha =x\cdot \tan 30°=8\cdot \tan 30°=8\cdot 0.57735=4.6188\text{m} \\ z=\sqrt{x^2+y^2}=\sqrt{8^2+4.6188^2}\doteq 9.2376\text{m} \\ h=y+z=4.6188+9.2376=8\sqrt{3}=13.8564\text{m} \end{gathered}$$

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