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 29.3°. approximate the height of the tower to the nearest foot.

feet (round to the nearest foot.)

Explanation:

Step1: Set up the tangent - ratio equation

We know that in a right - triangle formed by the tower, the ground, and the line of sight, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let $h$ be the height of the tower. The angle of elevation $\theta = 29.3^{\circ}$ and the adjacent side to the angle of elevation is $x = 5280$ feet. So, $\tan(29.3^{\circ})=\frac{h}{5280}$.

Step2: Solve for $h$

Multiply both sides of the equation by 5280: $h = 5280\times\tan(29.3^{\circ})$.
We know that $\tan(29.3^{\circ})\approx0.5609$. Then $h = 5280\times0.5609=5280\times\frac{5609}{10000}=5280\times0.5609 = 2961.552$.

Step3: Round the result

Rounding 2961.552 to the nearest foot gives $h\approx2962$ feet.

Answer:

2962