Question

# A 6 feet tall man finds an apple on the ground 6√3 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 6√3  feet away from the apple. Therefore, we can say that, AB = 6 feet and BC = 6√3  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                   =1√3                  θ = 30∘                               = tan(30∘)                               = 30∘

Suggest corrections

Similar questions
View More

People also searched for
View More