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Question

A 6 feet tall man finds an apple on the ground 63 feet away from him. What is the angle of depression when he is looking at the apple


__ in degrees ?


Solution

Imagine the man standing to be a vertical straight line, AB, and the position of the apple to be at a point C.

Now if we connect the man’s head and feet to the position of the apple we can imagine it to be a right triangle with vertices ABC.

We already know that the height of the man is 6 feet and he is standing 63  feet away from the apple. Therefore, we can say that, AB = 6 feet and BC = 63  feet.

The angle of depression is the angle the line of sight makes with the horizontal level, i.e. the angle AC and AD. Let us name the angle θ.

DAB = CBA = 90.

Therefore we can say that DA BC.

Now we can say that  DAC =  ACB, because they are alternate interior angles of the parallel lines AD and BC.

Let’s apply trigonometric ratios in the right triangle ABC to find θ

                tan θ = ABBC

                  =13

                 θ = 30

                              = tan(30)

                              = 30

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