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In the diagram below, ABCD is a square. Find \(\sin \angle PAQ.\)

 Mar 24, 2024
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Get the measure of the angles on either side of PAQ   

then subtract them from 90o to leave the size of PAQ.  

 

tangent of BAP is 5 / 7  =  0.7143   

tangent of DAQ is 5 / 7  =  0.7143  

 

note that tan–1(0.7143)  =  35.54o  

 

BAP + DAQ  =  35.54o + 35.54o  =  71.08o  

 

PAQ  =  90o – 71.08o  =  18.92o  

 

sin(18.92o)  =  0.324  

.

 Mar 24, 2024

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