A tower stands vertically on the ground. From a point on the ground which is 28.6m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45°. Find the height of the tower.

The correct option is 28.6 m.

Step-by-Step Explanation:

1. Understand the Situation:

Let us model the tower and the ground as a right-angled triangle:

• Let the height of the tower be h meters (the opposite side to the angle of elevation).

• The distance from the point on the ground to the foot of the tower is given as 28.6 m (the adjacent side to the angle of elevation).

• The angle of elevation of the top of the tower from this point on the ground is 45°.

2. Use the Trigonometric Ratio:

In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side:

$\tan =\frac{\text{Height of the tower}}{\text{Distance from the foot}}$

3. Substitute the Known Values:

We know that $\tan =1$.

Substituting the values into the formula:

$1=\frac{h}{28.6}$

4. Solve for the Height (h):

Multiply both sides by 28.6:

$h=28.6\text{m}$

Thus, the height of the tower is 28.6 m.