Geometry

 

What is the sine of an acute angle whose cosine is \frac{5}{7}?    

 

cosine is adjacent over hypotenuse    

 

given that the adjacent side is 5 and the hypotenuse is 7    

 

by Pythagoras, the opposide side is sqrt(7² – 5²) = sqrt(24)    

 

sine is opposite over hypotenuse    

 

so the sine is sqrt(24) / 7  =  2 • sqrt(6) / 7  or  ≈ 0.6999    

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