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 ${30}^{\circ }$ with it. The distance between the foot of the tree to the point where the top touches the ground is 12 m. Find the height of the tree.

• A. 12 m
• B. 4 m
• C. 4√3 m
• D. 12√3 m

Answer 1

The correct option is D

12√3 m

The given situation can be represented by the figure below

$cos\angle ACB=\frac{BC}{AC}$
$\Rightarrow cos{30}^{\circ }=\frac{BC}{AC}\Rightarrow \frac{\sqrt{3}}{2}=\frac{12}{AC}$
$\Rightarrow AC=\frac{24}{\sqrt{3}}=8\times \frac{3}{\sqrt{3}}=8\sqrt{3}m$
$tan\left(\angle ACB\right)=\frac{AB}{BC}\Rightarrow tan{30}^{\circ }=\frac{AB}{12}\Rightarrow AB=\frac{12}{\sqrt{3}}=4\sqrt{3}m$
$\therefore$ The height of tree was originally $AB+AC=4\sqrt{3}+8\sqrt{3}=12\sqrt{3}m.$