Question

A man from the top of a 100 metre high tower looks a car moving towards the tower at an angle of depression of 30^o. After some time, the angle of depression becomes 60^o. The distance (in metre) travelled by the car during this time is

• A. $100 \sqrt { 3 }$
• B. $\frac { 200 \sqrt { 3 } } { 3 }$
• C. $\frac { 100 \sqrt { 3 } } { 3 }$
• D. $200 \sqrt { 3 }$

Answer 1

Answer: (B)

$\frac { 200 \sqrt { 3 } } { 3 }$

Answer 2

$d = A B = O A - O B$

$= 100 \left[ \cot 30 ^ { \circ } - \cot 60 ^ { \circ } \right]$

=$100 \left[ \sqrt { 3 } - \frac { 1 } { \sqrt { 3 } } \right] = \frac { 200 \sqrt { 3 } } { 3 }$

Metre