Two man are on the opposite sides of a tower. They measure the angles of elevation the top of the tower as `30^(@)" and "60^(@)`. If the height of the tower is 150 m, find the distance between the two men.

Explanation

To solve the problem, we need to find the distance between two men standing on opposite sides of a tower, given the angles of elevation to the top of the tower and the height of the tower. Let's break down the solution step by step.

### Step 1: Understand the Problem
We have a tower of height \( AD = 150 \) m. Two men are standing at points \( B \) and \( C \) on opposite sides of the tower. The angle of elevation from point \( B \) to the top of the tower \( A \) is \( 60^\circ \), and the angle of elevation from point \( C \) to the top of the tower \( A \) is \( 30^\circ \).

### Step 2: Set Up the Triangles
We will use right triangle trigonometry to find the distances \( BD \) and \( CD \):
- In triangle \( ABD \) (where \( A \) is the top of the tower, \( B \) is the point on the ground near the tower, and \( D \) is the foot of the tower):
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