Question

The angle of elevation of the top of a tower at a distance 30 m from its foot on a horizontal plane is found to be 30${}^o$. The height of the tower is _____

• A. $17.3$ m
• B. $57.96$ m
• C. $17.8$ m
• D. $173$ m

Answer 1

The correct option is A $17.3$ m

Let AB be the tower and O be the point of observation,

then OA = 30 m and $\angle$AOB = 30${}^o$

$\therefore$ In $△$OAB, tan 30${}^o$ =

$\frac{AB}{OA}\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{30}\Rightarrow AB=\frac{30}{\sqrt{3}}$

$\therefore$ AB = $\frac{30\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$ = 10$\sqrt{3}$ = 10 x 1.73 = 17.3

$\therefore$ Height of the tower is 17.3 m.