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

The Correct Option is B

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.