Question

In the adjoining figure, the angle of elevation of the point C from the point B, is :

• A. 30°
• B. 45°
• C. 22.5°
• D. 67.5°

Hint:

If the height is smaller than the base, the angle of elevation is always less than \(45^\circ\). If they are equal, the angle is exactly \(45^\circ\).

Answer 1

The Correct Option is A

To solve this problem, we need to find the angle of elevation from point B to point C in the given right-angled triangle. The triangle is shown below:

Given:

• At point A, the angle is 90°.
• The angle at point C is marked as \(3x\).
• The angle at point B is marked as \(x\).

In any triangle, the sum of all angles is 180°. For this right-angled triangle:

\(90^\circ + 3x + x = 180^\circ\)

Solving for \(x\):

\(90^\circ + 4x = 180^\circ\) \(4x = 180^\circ - 90^\circ\) \(4x = 90^\circ\) \(x = \frac{90^\circ}{4}\) \(x = 22.5^\circ\)

Since \(x = 22.5^\circ\), the angle at point B is \(22.5^\circ\).

The angle at point C is \(3x\), which calculates as:

\(3x = 3 \times 22.5^\circ = 67.5^\circ\)

Therefore, the angle of elevation of point C from point B is:

\(67.5^\circ\)

The correct answer is:

67.5°

(Note: The correct answer listed above as 30° should be updated as 67.5° based on calculations.)