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Question

# A 6 feet tall man sees an apple on the ground, 6√3 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 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, 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 angled triangle △ABC to find θ. tanθ=ABBC =66√3 =1√3 We know that tan(30∘)=1√3 θ=30∘

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