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Question

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

A
30
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B
60
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C
45
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D
can't be determined
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Solution

The correct option is A 30
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, as in fig(i).
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 when the point is below the horizontal level, i.e. the angle DAC.
Let ACB= θ, as in fig(ii).
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 ΔABC to find θ.

tanθ=ABBC
=663
=13
We know that tan(30)=13
θ=30
So, the angle of depression when he is looking at the apple is 30

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