Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are `30^0a n d45^0` respectively. If the distance between two boats is 100m, find the height of the light house.

Explanation

To solve the problem step by step, we will use trigonometric ratios to find the height of the lighthouse based on the angles of elevation from the two boats.

### Step 1: Define the Variables
Let:
- \( H \) = height of the lighthouse
- \( x \) = distance from the first boat (where the angle of elevation is \( 45^\circ \)) to the base of the lighthouse
- Therefore, the distance from the second boat (where the angle of elevation is \( 30^\circ \)) to the base of the lighthouse will be \( 100 - x \).

...