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
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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 :
