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In the diagram, ABCD  is a square. Find Sin PAQ

 Jun 29, 2024
edited by jumbean  Jun 29, 2024
edited by jumbean  Jun 29, 2024
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PA = sqrt (5^2 + 7^2)  = sqrt  74 = AQ

PQ = sqrt (2^2 + 2^2)  = sqrt 8

 

Law of Cosines

 

PQ^2  = PA^2 + PQ^2  - 2(PA * PQ)  cos (PAQ)

 

8 = 74 + 74  - 2 ( 74)  cos (PAQ)

 

cos (PAQ)  =  [ 8 - 74 -74 ] / [ -2 * 74 ]   =  35 / 37

 

sin (PAQ)  = sqrt [ 37^2 - 35^2 ] /  37 =  sqrt [ 144 ] / 37 =   12 / 37

 

cool cool cool

 Jun 30, 2024

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