Angle Between Two Lines

Given:

- Height of the building = m
- Angle of elevation to the top of the lighthouse =
- Angle of depression to the base of the lighthouse =

Step 1: Define Variables

Let the height of the lighthouse be meters, and let the horizontal distance between the lighthouse and the building be meters.

Step 2: Use the Tangent Function

For the angle of elevation to the top of the lighthouse: For the angle of depression to the base of the lighthouse:

Step 3: Solve for

Step 4: Compute the Difference in Heights

Final Answer: 20 m

Given:

Two towers of heights and subtend angles of and respectively at the midpoint of the line segment joining their feet.

Step 1: Define the Right Triangles

Let the distance from the midpoint to the base of each tower be . Then, using the tangent function:

Step 2: Solve for Heights

We know: So,

Step 3: Compute the Ratio

Final Answer: 3:1