A flagstaff stands in the centre of a rectangular field whose diagonal is 120 m. It subtends angles of `15^@` and `45^@` at the midpoints of the sides of the field. The height of the flagstaff is

Options

A. 20m
B. `30sqrt(2+sqrt3)m`
C. `30sqrt(2-sqrt3)m`
D. 40m

Explanation

To solve the problem step by step, we will use trigonometric ratios and the Pythagorean theorem.

### Step 1: Understanding the Problem
We have a rectangular field with a diagonal of 120 m. A flagstaff stands at the center of this field and subtends angles of 15° and 45° at the midpoints of the sides of the rectangle. We need to find the height of the flagstaff.

### Step 2: Setting Up the Diagram
Let:
- \( H \) be the height of the flagstaff.
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