Question

1. the tallest television transmitting tower in the world is in north dakota, and it is 2059 feet tall. if you are on level ground exactly 5280 feet (one mile) from the base of the tower, what is your angle of elevation looking up at the top of the tower? show your work #6 21.30 67.05 68.70 22.95 * please answer all required questions

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the height of the tower is the opposite side (\(h = 2059\) feet) and the distance from the base of the tower is the adjacent side (\(d=5280\) feet). Let the angle of elevation be \(\theta\). So, \(\tan\theta=\frac{2059}{5280}\).

Step2: Calculate the value of \(\tan\theta\)

\(\tan\theta=\frac{2059}{5280}\approx0.39\).

Step3: Find the angle \(\theta\)

We know that \(\theta=\tan^{- 1}(0.39)\). Using a calculator, \(\theta\approx21.30^{\circ}\) (make sure the calculator is in degree mode).

Answer:

\(21.30\)