Question

A tower stands vertically on the ground. From a point on the ground, which is 30 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be ${30}^{\circ }$. Find the height of the tower.

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

Answer 1

The correct option is C

10$\sqrt{3}$ m

The given situation can be represented by the $\Delta$ below

Now, $tan{30}^{\circ }=\frac{AB}{BC}\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{30}\Rightarrow 10\sqrt{3}=AB\therefore Heightoftoweris10\sqrt{3}m$