Question

From the top of a house $32$ meters high, if the angle of elevation of the top of a tower is ${45}^0$ and the angle of depression of the foot of the tower is ${30}^0$, then the height of the tower is

• A. $\frac{32}{\sqrt{3}}(\sqrt{3}+1)$ meters
• B. $32(\sqrt{3}+1)$ meters
• C. $32\sqrt{3}$ meters
• D. $\frac{32}{3}(\sqrt{3}+1)$meters

Answer 1

The correct option is B $32(\sqrt{3}+1)$ meters

From $\Delta OBH$,
$\frac{BH}{OB}=\cot {30}^0=\sqrt{3}$
or $BH=32\sqrt{3}$
From $\Delta BHT$,
$BT=BH=32\sqrt{3}$
$\therefore$ Height of tower $=OT=OB+BT=32(\sqrt{3}+1)$ metres

Hence, option B.