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

Step 1: Understanding the Concept:
The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal level.
Step 2: Key Formula or Approach:
In a right-angled triangle, if we know the height (\(h\)) and the base (\(b\)): \[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\text{Height}}{\text{Base}} \]
Step 3: Detailed Explanation:
Assuming the figure provides a height \(h\) and base \(b = h\sqrt{3}\):
1. Let the angle of elevation be \(\theta\).
2. \(\tan \theta = \frac{h}{h\sqrt{3}}\).
3. Simplify: \(\tan \theta = \frac{1}{\sqrt{3}}\).
4. Therefore, \(\theta = 30^\circ\).
Step 4: Final Answer:
The angle of elevation is 30°.