Question

Calculating a Distance Observersat P and Q are located on the sideof a hill that is inclined 32° to thehorizontal, as shown. The observerat P determines the angle ofelevation to a hot-air balloon to be62º. At the same instant theobserver at Q measures the angleof elevation to the balloon to be71°. If P is 60 m down the hillfrom Q, find the distance from Qto the balloon.

Answer 1

To solve this problem, we will first have to visualize the problem and analyze the angles.

The angle at the hill is at 32 degrees and it is alternate to an angle at P, and performing other angles analysis as seen below:

The final drawing, that will help us find the distance between Q and the ballon will look like:

So in solving for the distance from Q to the ballon, we will use the sine rule:

`\begin{gathered} (60)/(\sin9)=(QB)/(\sin 30) \\ QB=(60\sin 30)/(\sin 9) \\ QB=(30)/(\sin 9) \\ QB=191.77m \end{gathered}`

The distance from Q to the ballon is 191.77m