Question

The angles of elevation of the top of a tower, from the top and the foot of a pole of height 10 m, are 300 and 600 respectively. The height of the tower is

• A. 20m
• B. 15m
• C. 10m
• D. None of these

Answer 1

Answer: (B)

15m

Answer 2

Assuming the height of tower be h metres.
tan 30 = $\frac{1}{\sqrt 3} = \frac{(h-10)}{base}$
base = $(h-10)\times\sqrt3$
tan 60 = $\frac{h}{base}$
base = $\frac{h}{\sqrt3}$
So, $(h-10) \times \sqrt3 = \frac{h}{\sqrt3}$
$3h - 30 = h$
h = 15 metres,

Therefore, height of tower is 15 metres.