# Basic Trigonometric Ratios

### Real life example using the trigonometric ratios

Distance measuring equipment is standard on commercial aircraft. This measures the distance between the plane and radar station. If the distance from the plane to a radar station is \(160\) kilometres, and the angle of depression is \(33^{\circ}\), what is the distance (in kilometres) of the point directly below the plane to the radar station.

Firstly it is always important to draw the picture of the situation.

\begin{eqnarray*}

\sin 57^{\circ} &=& \frac{x}{160} \\

x &=& 160 \times \sin 57^{\circ} \\

&\approx& 134.187~\mbox{km}

\end{eqnarray*}

Therefore, the distance of the point directly below the plane to the radar station is approximately \(134.2 \mbox{ km.}\)