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# help

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Esther ran 6km due north from point p to point q. she then changed direction and ran 4km to point r. she was then 3km from her starting point p.

a) work out the bearing of point r from point q. give your answer correct to the nearest degree.

b) work out the bearing of point r from point p. give your answer correct to the nearest degree

Jan 28, 2018

### 1+0 Answers

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a)  Here, we are trying to find angle PQR.....we can use the Law of Cosines for this...so we have...

3^2  =  6^2 + 4^2  - 2(6)(4)cosQPR    rearrange as

[ 3^2 - 6^2 - 4^2 ] / [ - 2(6)(4)]  =  cos QPR

Using the cosine inverse (arccos), we have that

arccos ( [ 3^2 - 6^2 - 4^2 ] / [ - 2(6)(4)] )  = QPR ≈  26.38°

So....the bearing of R from Q  =  [180 - 26.38]°  ≈  153.62°  = 154°

b) This one is easier...here we are trying to find angle QPR.....we can still use the Law of Cosines

4^2 =  6^2  +  3^2  - 2(6)(3)cos QPR   rearrange

([ 4^2 - 6^2 - 3^2 ] / [ -2(6)(3)] )  =  cosQPR

Using the cosine inverse (arccos), we have the bearing of R from P  is

arccos ([ 4^2 - 6^2 - 3^2 ] / [ -2(6)(3)] )  = QPR  ≈  36.34° = 36°

Here's a pic :    Jan 28, 2018