SSA and geometry

The distance between the points P and Q was 356 m measured in the terrain. The viewer can see the PQ line at a 107°22' viewing angle. The observer's distance from P is 271 m. Find the viewing angle of P and the observer.

Correct answer:

Q =  46.5966 °

Step-by-step explanation:

$$\begin{gathered} R=107+\frac{22}{60}=\frac{107\cdot 60}{60}+\frac{22}{60}=\frac{6420}{60}+\frac{22}{60}=\frac{6420+22}{60}=\frac{6442}{60}=\frac{3221}{30}\doteq 107.3667{}^{\circ } \\ r=356\text{m} \\ q=271\text{m} \\ \frac{\sin (Q)}{\sin (R)}=\frac{q}{r} \\ s=\sin (Q) \\ s=\frac{q}{r}\cdot \sin R=\frac{q}{r}\cdot \sin 107.36666666667°=\frac{271}{356}\cdot \sin 107.36666666667°=\frac{271}{356}\cdot 0.954414=0.72653 \\ Q=\frac{180°}{\pi }\cdot \arcsin s=\frac{180°}{\pi }\cdot \arcsin 0.7265=46.5966^{\circ }=46°35^{\prime }48" \end{gathered}$$

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