Question

In the figure, the angles of depressions of point O as seen from points A and P are:

• A. 30°, 45°
• B. 45°, 30°
• C. 45°, 60°
• D. None of these

Hint:

The angle of depression from a point is equal to the angle of elevation from the point directly below it.

Answer 1

The Correct Option is B

In the given diagram, we are asked to find the angles of depression of point \( O \) as seen from points \( A \) and \( P \). The angle of depression is measured from the horizontal, which means the angle formed between the line of sight from the point and the horizontal line at the eye level. - From point \( A \), the angle of depression is the angle between the horizontal line and the line connecting point \( A \) to \( O \). Since we are given \( \angle OAB = 45^\circ \), by alternate interior angles, the angle of depression from point \( A \) is also \( 45^\circ \). - From point \( P \), the angle of depression is the angle between the horizontal line at \( P \) and the line connecting \( P \) to \( O \). Given that the angle \( \angle POQ = 60^\circ \), and since alternate interior angles are congruent, the angle of depression from point \( P \) is \( 30^\circ \).
Step 1: Conclusion.
Therefore, the angles of depression from points \( A \) and \( P \) are \( 45^\circ \) and \( 30^\circ \), respectively.