Question

the tallest television transmitting tower in the world is in north dakota. from a point on level ground 5280 feet (one mile) from the base of the tower, the angle of elevation is 24.9°. approximate the height of the tower to the nearest foot. feet (round to the nearest foot.)

Explanation:

Step1: Set up tangent - ratio equation

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the tower be $h$. The angle of elevation $\theta = 24.9^{\circ}$ and the adjacent side to the angle of elevation is the distance from the point on the ground to the base of the tower, which is $5280$ feet. So, $\tan(24.9^{\circ})=\frac{h}{5280}$.

Step2: Solve for $h$

Multiply both sides of the equation by $5280$: $h = 5280\times\tan(24.9^{\circ})$.
We know that $\tan(24.9^{\circ})\approx0.4647$. Then $h = 5280\times0.4647$.
$h=5280\times0.4647 = 2451.616$.

Answer:

$2452$