Question

A man at the top of a vertical lighthouse observes a boat coming directly towards it if it takes $20$ minutes for the angle of depression to change from ${30}^{\circ }to{60}^{\circ }$ the time taken by the boat to reach the lighthouse from the point when the angle of depression was ${30}^{\circ }$ is

• A. $30$ Minutes
• B. $20$ Minutes
• C. $10$ Minutes
• D. $5$ Minutes

Answer 1

The correct option is A $30$ Minutes

Given
$d=20minutes$
${\theta }_1={30}^{\circ }$
${\theta }_2={60}^{\circ }$
Formula is $b=\frac{d\cot {\theta }_2}{\left(\cot {\theta }_1-\cot {\theta }_2\right)}$
By putting the values from the given question, we get $b=10minutes$
So the time taken by the boat to reach the lighthouse from the point when the angle of depression was ${30}^{\circ }$ is $=d+b=20+10=30minutes$