A man on a cliff observes a boat at an angle of depression of 300 which is approaching the shore - Maths - Some Applications of Trigonometry

Question

A man on a cliff observes a boat at an angle of depression of
300 which is approaching the shore to the point
immediatly beneath the observer with a uniform speed Six minutes
later,the angle of depression of the boat is found to be
600 Find the time taken by the boat to reach the
shore

Ayush Jha · Accepted Answer

We have-

Let the uniform velocity be v and the the distance to be travelled by the boat to reach the soar be x So, $\tan 30^{0} = \frac{h}{6 v + x} \frac{1}{\sqrt{3}} = \frac{h}{6 v + x}$ (1) Similarly, $\tan 60^{0} = \frac{h}{x} \sqrt{3} = = \frac{h}{x}$ (2) Divide equation(1) by (2) to get, $x = 3 v$ Hence the time taken to reach the soar is 3 minutes

A man on a cliff observes a boat at an angle of depression of 300 which is approaching the shore to the point immediatly beneath the observer with a uniform speed. Six minutes later,the angle of depression of the boat is found to be 600.Find the time taken by the boat to reach the shore.

A man on a cliff observes a boat at an angle of depression of 30⁰ which is approaching the shore to the point immediatly beneath the observer with a uniform speed. Six minutes later,the angle of depression of the boat is found to be 60⁰.Find the time taken by the boat to reach the shore.