Aman lying down on a top of a cliff 40m observes angle of depression of a buoy to be 20° if he is in line with the buoy calculate distance between buoy and the feet of the cliff (which may be assumed to be vertical)

Explanation:

In order to solve this problem, the figure attached will be helpful.

As we can see, the angle of depression (below the horizontal line) is , if we know the angle between the horizontal and the ground (bottom of the cliff) is , by simple geometry we will know the other angle is :

Now, we have a right triangle here and we need to find which is istance between buoy and the feet of the cliff, and we can solve this by using the tangent trigonometric function:

  (1)

Where:

Rewritting equation (1):

  (2)

Finding :

  (3)

>>>distance between buoy and the cliff

its ok