An observer 2 m tall is 10 3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The height of the tower is:

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& SR=PQ=2m\\ & PS=QR=10\sqrt{3}m\\ & \tan 30^{\circ }=\frac{TS}{PS}\\ & \frac{1}{\sqrt{3}}=\frac{TS}{10\sqrt{3}}\\ & TS=\frac{10\sqrt{3}}{\sqrt{3}}=10m\\ & TR=TS+SR=10+2=12m\end{array}$$