Question

The angle of elevation of the top of a pillar at any point A on the ground is 15^o. On walking 40 metre towards the pillar, the angle becomes 30^o. The height of the pillar is

• A. 40 metre
• B. 20 metre
• C. $20 \sqrt { 3 }$ metre
• D. $\frac { 40 } { 3 } \sqrt { 3 }$ metre

Answer 1

Answer: (B)

20 metre

Answer 2

$40 = h \left[ \cot 15 ^ { \circ } - \cot 30 ^ { \circ } \right]$

$h = \frac { 40 } { \cot 15 ^ { \circ } - \cot 30 ^ { \circ } }$

$h = \frac { 40 } { \frac { 1 } { 2 - \sqrt { 3 } } - \sqrt { 3 } }$ $= \frac { 40 ( 2 - \sqrt { 3 } ) } { 4 - 2 \sqrt { 3 } }$

$h = 20$metre