Question #37bed

1 Answer
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)