Question

The height of a tree is 10$\sqrt{3}$ m, if a boy looks at the top of the tree with an angle of elevation of ${30}^{\circ }$, find the distance between the boy and the tree.

• A. 10 m
• B. 10$\sqrt{3}$ m
• C. 30 m
• D. 20 m

Answer 1

The correct option is C

30 m

The given figure illustrates the scenario mentioned in the question :
Given, the tree is having a height of $10\sqrt{3}m.$

So, AB = $10\sqrt{3}m.$

In Triangle ABC,
$\tan {30}^{\circ }=\frac{AB}{BC}=\frac{1}{\sqrt{3}}\Rightarrow BC=10\sqrt{3}\times \sqrt{3}\Rightarrow BC=30m.$