an aircraft flew 80km from a harbor P on a bearing of 36degree to Q and 200km on a bearing of 125 to another harbor R.what is the distance between P and R,bearing of P from R and R?

Question

Find the bearing and distance with full workings pls

Answer 1

Bearings are in relation to north. In the triangle PQR, angle Q=36+180-125=91 degrees.

Using the cosine rule, PR^2=PQ^2+QR^2-2PQ.QRcosQ=6400+40000-2*16000cos91=46958.48 approx.

Therefore PR=216.7km approx.

We can find other angles in PQR using the sine rule, so sinP/200=sin91/216.7=0.004614.

sinP=200*0.004614=0.9228 approx.

From this P=67.34º. To find the bearing we need to add 36º, the initial bearing of Q from P=103.34.

Comments

This answer was revised to correct a few errors and to insert the diagram. Apologies to uche for the errors.