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 20.7°. 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, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the tower be $h$. The angle of elevation $\theta = 20.7^{\circ}$ and the adjacent side to the angle of elevation is $x = 5280$ feet. So, $\tan(20.7^{\circ})=\frac{h}{5280}$.

Step2: Solve for $h$

Multiply both sides of the equation by 5280: $h = 5280\times\tan(20.7^{\circ})$.
We know that $\tan(20.7^{\circ})\approx0.3805$. Then $h = 5280\times0.3805= 5280\times\frac{3805}{10000}= \frac{5280\times3805}{10000}=\frac{20080400}{10000}=2008.04$.

Step3: Round the result

Rounding 2008.04 to the nearest foot gives $h\approx2008$ feet.

Answer:

2008