Question

Two weather tracking stations are on the equator 159 miles apart. A weather balloon is located on a bearing of N 38°E from the western station and on a bearing of N 14°E from the eastern station. How far is the balloon from the western station?

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Redraw the given triangle

STEP 2: Write the needed measures

$\begin{gathered} A=90-38=52^{\circ}----Right\text{ angle} \\ B=90^{\circ}+14^{\circ}=104^{\circ} \\ C=180-104^{\circ}-52^{\circ}=24^{\circ} \\ c=159miles \\ b=required\text{ side} \end{gathered}$

STEP 3: State the Sine rule

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

STEP 4: Substitute the known measures into the formula

$\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin104}{b}=\frac{\sin24}{159} \\ Cros\text{s multiply} \\ b\cdot\sin24=159\cdot\sin104 \\ b=\frac{159\cdot\sin104}{\sin24} \\ b=\frac{154.2770205}{0.406736643}=379.3044544 \\ b\approx379.3\text{ miles} \end{gathered}$

Hence, the balloon is approximately 379.3 miles away from the western station.