If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is , then the height of the hill is

Explanation: 1. Geometric Interpretation: Let be the height of the hill and be the foot of the hill on the horizontal plane. Let the top of the hill be . Since the angle of elevation from each vertex and to the top is the same ( ), the distances from the foot of the hill to each vertex must be equal. This means that is the circumcenter of the triangle , and is the circumradius . 2. Relationship between Height and Circumradius: In the right-angled triangle (where and ): 3. Using the Sine Rule: From the properties of a triangle and the Sine Rule, we know: From this, we can express the circumradius as: 4. Final Calculation for Height ( ): Substitute the value of into the height equation: Correct Option: D.

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