SOLUTION: angle PQR = angle PSQ = 90° |PS| =9cm, |SR| =16cm. calculate the value of SQ and and angle QRS.

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Question 1132346: angle PQR = angle PSQ = 90° |PS| =9cm, |SR| =16cm. calculate the value of SQ and and angle QRS.
Answer by MathLover1(20850) About Me  (Show Source):
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if PSQ+=+90°, than RSQ=90°
=> triangle PSR+is similar to triangle RSQ, corresponding sides are proportional
=> side SR=+16cm is common side
=>+SR%2FPS=SR%2FSQ
=> 16%2F9=16%2FSQ
=> 16SQ=16%2A9
=> SQ=16%2A9%2F16
=> SQ=9cm
then angle QRS is:
tan%28QRS%29=SQ%2FSR=9%2F16=0.5625
angle QRS=tan%5E-1%280.5625%29=29.36°