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What is the angle of elevation of point A from C and angle of depression of point D from A?

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90 ° − ϕ

θ

°

2 θ

°

90^{\circ} - θ

°

θ

answer is A.

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Detailed Solution

We need to find the angle of elevation of point A from C and angle of depression of point D from A.
Angle of elevation and angle of depression are equal.
We have the figure,
Question Image

Let

α

be the angle of elevation of point A from point C. Since the sum of interior angles of a triangle is

180 °

, the sum of angle

α

and

ϕ

will be

90 °

. We calculate the angle of elevation of point A from C,

α = ∠ A C B ⇒ α = 90 ° − ϕ

Let

β

be the angle of depression of point D from point A. The angle of elevation and the angle of depression are equal,

β = θ

Thus, the angle of elevation of point A from point C is

90 ° − ϕ

and the angle of depression of point D from point A is

θ

.
Therefore, option 1 is correct.

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