Question

An object is observed from the points A, B and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at A is \( \theta \), at B is \( 2\theta \), and at C is \( 3\theta \). If AB = a, BC = b, and the height of the object is h, then the height of the object is

• A. \( \frac{a}{2} \left( b - a \right) \)
• B. \( \frac{a}{2b} \left( b - a \right) \)
• C. \( \frac{b}{2a} \left( b - a \right) \)
• D. \( \frac{2a}{b} \left( b - a \right) \)

Hint:

When dealing with objects at different points, use trigonometric functions to relate the angles and distances to calculate the height.

Answer 1

The Correct Option is A

Step 1: Use trigonometry.
Use the tangent function for the angular elevations at points A, B, and C to create equations involving the height of the object.
Step 2: Conclusion.
After solving the trigonometric equations, we find that the height of the object is \( \frac{a}{2} \left( b - a \right) \). Final Answer: \[ \boxed{\frac{a}{2} \left( b - a \right)} \]