Question

A point Q is 24 km away and at a bearing of 072 degrees from P. From Q a man walks at a bearing of 320 degrees, to a point R, located directly north of P. Calculate the distance of PR and QR.

Answer 1

Answer:

RQ=35.51 km

PR=34.62 km

Step-by-step explanation:

Bearing of Q from P = 72 degrees

• The complementary angle of 72 degrees is 18 degrees.
• Using alternate angles, we get the first angle at Q to be 18 degrees.

Bearing of R from Q=320 degrees

320=270+50

Therefore, the second angle of Q is 50 degrees.

$\angle P=72^\circ\\\angle Q=68^\circ\\\angle R=180^\circ-(72^\circ+68^\circ)=40^\circ$

Using Law of Sines

$\dfrac{r}{\sin R} =\dfrac{p}{\sin P} \\\dfrac{24}{\sin 40} =\dfrac{p}{\sin 72} \\p=\sin 72 \times \dfrac{24}{\sin 40}\\\\p=RQ=35.51 km$

Using Law of Sines

$\dfrac{q}{\sin Q} =\dfrac{r}{\sin R} \\\dfrac{q}{\sin 68} =\dfrac{24}{\sin 40} \\q=\dfrac{24}{\sin 40}\times \sin 68\\\\q=PR=34.62 km$