Answer to Question #101063 in Trigonometry for Poornima

Question

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

Answer 1

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 $=$ $\sqrt{106.74}$

PR $\approx$ 10.33 Km

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