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?.

1 Answer
May 26, 2018

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

Explanation:

"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"