Question

In the figure, the angles of depression 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:

Angle of depression = Angle of elevation (measured from the horizontal line). Always look for alternate interior angles when such problems involve parallel lines.

Answer 1

The Correct Option is C

Step 1: Understanding the figure.
The figure shows two points \( A \) and \( P \) vertically above points \( B \) and \( Q \), respectively, with \( O \) as the observation point. The lines \( OA \) and \( OP \) are inclined at angles of \( 45^\circ \) and \( 60^\circ \) with the horizontal.

Step 2: Relation between line of sight and angle of depression.
In a right-angled triangle, the angle of depression from a point above the horizontal is equal to the angle of elevation from the point below (alternate interior angles).

Step 3: Identify angles.
From the figure: - Angle at \( O \) corresponding to \( A \) is \( 45^\circ \). - Angle at \( O \) corresponding to \( P \) is \( 60^\circ \).

Step 4: Hence,
The angles of depression of point \( O \) from \( A \) and \( P \) are \( 45^\circ \) and \( 60^\circ \), respectively.
Step 5: Final Answer.
\[ \boxed{45^\circ, 60^\circ} \]