Question

A blimp provides aerial television views of a tennis match. The television is camera sights the stadium at a 14. angle of depression. Thealtitude of the blimp is 400 meters. What is the line of sight distance from the television camera to the base of the stadium?

Answer 1

Answer:

1653.426 meters.

Explanation:

The diagram below represents the given problem:

The line of sight is the hypotenuse of the right triangle labeled x above.

Using trigonometric ratios:

$\begin{gathered} \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \implies\sin 14\degree=\frac{400}{x} \end{gathered}$

We solve for x:

$\begin{gathered} x\times\sin 14=400 \\ x=\frac{400}{\sin 14\degree} \\ x=1653.426m \end{gathered}$

The line of sight distance from the television camera to the base of the stadium is 1653.426 meters.