Question #101063
A car drives 15 km on a bearing of 114 degrees from P to Q. It then changes direction and drives 18 km on a bearing of 329 degrees from Q to R.find the distance between P to R
1
Expert's answer
2020-01-08T12:13:17-0500



Step 1: To find the distance between P and R first draw the explanatory diagram as mentioned below:





Step 2:


From point Q the car has a bearing of 329°\degree == 270°\degree + 59°\degree

From the above figure we can see

\angle RQP == 59°\degree - 24°\degree

\angle RQP == 35°\degree


Step 3:


Now in \triangle PQR we can use the cosine formula to fine the distance between P to R:


PR2 == PQ2 ++ QR2 - 2(PQ)(QR)Cos35°\degree // \angle RQP = 35°\degree

== 152 ++ 182 - 2*15*18* 0.819 // Cos35°\degree = 0.819


== 225 ++ 324 - 442.26


== 549 - 442.26

PR2== 106.74


PR == 106.74\sqrt{106.74}


PR \approx 10.33 Km


Answer : Distance between P and R is approximately 10.33 Km.


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