A vertical tower stands on a declivity which isinclined at `15^@` to the horizon. From the foot of the tower a man ascends the declivity from 80 feet and then finds that the tower subtends an angle of `30^@`. The height of the tower is

Options

A. `40(sqrt(6)+sqrt(2))`
B. `20(sqrt(6)-sqrt(2))`
C. `40(sqrt(6)-sqrt(2))`
D. `80(sqrt(6)-sqrt(2))`

Explanation

To solve the problem, we need to find the height of the vertical tower (let's denote it as \( H \)) given the information about the declivity and the angle subtended by the tower.

### Step-by-step Solution:

1. **Understand the Geometry**:
- Let \( A \) be the top of the tower, \( B \) be the foot of the tower, and \( C \) be the point where the man is standing after ascending the declivity.
- The angle of inclination of the declivity is \( 15^\circ \) and the angle subtended by the tower at point \( C \) is \( 30^\circ \).
- The distance \( BC \) (the distance ascended by the man) is \( 80 \) feet.
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