Question #37bed

1 Answer
Olivier B.
Jun 12, 2015

The correct answer is #hat(QR)=cos^(-1)(12/13)#

Explanation:

First, notice that #5^2+12^2 = 25+144 = 169 = 13^2#
therefore, the triangle formed with P,Q and R is a right triangle, according to the reverse of the pythagorean theorem.

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In this triangle, we have:

#cos(hat(PR))=P/R#

#sin(hat(PR))=Q/R#

#cos(hat(QR))=Q/R#

#sin(hat(QR))=P/R#

Therefore, the angle #hat(QR)# is found with

#cos(hat(QR))=Q/R=12/13#

#rarr hat(QR)=cos^(-1)(12/13)#

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