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 20.5°. approximate the height of the tower to the nearest foot.

□ feet (round to the nearest foot.)

Explanation:

Step1: Recall tangent - function formula

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the tower be $h$ (opposite side) and the distance from the base of the tower be $d = 5280$ feet (adjacent side), and the angle of elevation $\theta=20.5^{\circ}$. So, $\tan\theta=\tan(20.5^{\circ})=\frac{h}{d}$.

Step2: Solve for $h$

Since $d = 5280$ and $\tan(20.5^{\circ})\approx0.3739$, we can rewrite the equation as $h = d\times\tan\theta$. Substituting the values, we get $h=5280\times\tan(20.5^{\circ})$.
$h = 5280\times0.3739=1973.192$.

Step3: Round the result

Rounding $1973.192$ to the nearest foot, we get $h\approx1973$.

Answer:

1973