From the top of aspier the angle of depression of the top and bottom of a tower of height h are `theta` and `phi` respectively. Then height of the spier and its horizontal distance from the tower are respectively.

Options

A. `(hcos theta sin phi)/(sin theta - phi)` and `(h cos theta cos phi)/(sin(theta - phi))`
B. `(h cos theta cos phi)/(sin(theta +phi)).(h tan theta cos phi)/(sin (theta + phi))`
C. `(h sin theta phi)/(sin(theta + phi)), (h cos theta cos phi)/(sin(theta + phi))`
D. None of these

Answer

To solve the problem step by step, we will use trigonometric relationships based on the angles of depression from the top of the spire to the top and bottom of the tower.

### Step 1: Understand the Diagram
1. Draw a diagram with a spire (point A) and a tower (point C) of height \( h \).
2. Let the height of the spire be \( x \).
3. The horizontal distance from the spire to the tower is \( d \).
4. The angle of depression to the top of the tower is \( \theta \) and to the bottom of the tower is \( \phi \).