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"#