Tower Height Calculation Using Trigonometry

The problem involves finding the height of a tower given the distance from its base and the angle of elevation to its top. This can be solved using basic trigonometry in a right-angled triangle.

Identifying the Triangle Components

Consider the right-angled triangle formed by:

• The tower's height (opposite side to the angle of elevation). Let this be '$h$'.
• The distance from the ground point to the foot of the tower (adjacent side to the angle of elevation). This is given as 28.6 m.
• The line of sight from the ground point to the top of the tower (hypotenuse).

The angle of elevation is given as 45°.

Applying the Tangent Function

The trigonometric function relating the opposite side, adjacent side, and the angle is the tangent:

$ \tan(\text{angle}) = \frac{\text{Opposite}}{\text{Adjacent}} $

Substituting the known values:

$ \tan(45^\circ) = \frac{h}{28.6 \text{ m}} $

Calculating the Tower Height

We know that $\tan(45^\circ) = 1$. Therefore, the equation becomes:

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

Solving for '$h$':

$ h = 1 \times 28.6 \text{ m} $

$ h = 28.6 \text{ m} $

The height of the tower is 28.6 m.