Justice starts a 5km walk from P on a bearing 023. He then walks 4km on a bearing of 113 to Q. What is the bearing of Q from P?.

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Answer 1 · 2018-05-26T15:47:37

$61^@39'35''$ $"Bearing P-Q"$

$"Let the turning point be R"$

$:.R-Q=113^@$ $"Given"$

$:.P-R=23^@$ $"Given"$

$:.R-P=23^@+180^@=203^@$

$:.203^@-113^@=90^@=angleR$

$:."in right"$ $triangle$ $"QPR"$ $:-$

$:.tan angle P=4/5=0.8 arctan=38^@39'35''=angle P$

$:.180^@-(90^@+38^@39'35'')=51^@20'25''=angle Q$

$:.113^@+180^@=293^@=" bearing Q-R"$

$:.293^@-51^@20'25''=241^@39'35''="bearing Q-P"$

$:."bearing P-Q"=241^@39'35''-180^@=61^@39'35''="bearing P-Q"$