Question

A vertical pole consists of two parts, the lower part being one third of the whole. At a point in the horizontal plane through the base of the pole and distance 20 metres from it, the upper part of the pole subtends an angle whose tangent is $\frac { 1 } { 2 }$ . The possible heights of the pole are

• A. 20m and$20 \sqrt { 3 }$m
• B. 20 m and 60 m
• C. 16 m and 48 m
• D. None of these

Answer 1

Answer: (B)

20 m and 60 m

Answer 2

$\frac { H } { 3 } \cot \alpha = d$ and $H \cot \beta = d$ or $\frac { H } { d } = \tan \beta$ ⇒ $1 + \frac { H ^ { 2 } } { 3 d ^ { 2 } } = \frac { 4 H } { d }$

⇒ $H ^ { 2 } - 4 d H + 3 d ^ { 2 } = 0$

⇒ $H = 20$ or 60 m.