SOLUTION: A right triangle has an area of 54 cm squared and one of the legs is 9 cm, what are the measures of the two acute angles to the nearest degree ?

Question 937621: A right triangle has an area of 54 cm squared and one of the legs is 9 cm, what are the measures of the two acute angles to the nearest degree ?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
area = ab/2
54 = 9b/2
b = 2*54/9
b = 12 cm
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c = sqrt( aa + bb )
c = sqrt( 9*9 + 12*12 )
c = 15 cm
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use law of sines to find the angles:
a/sinA = c/sinC
sinA/a = sinC/c
sinA = a*sinC/c
A = asin( a*sinC/c )
A = asin( 9*sin(90)/15 )
A = 36.8698976458
B = asin( 12*sin(90)/15 )
B = 53.1301023542
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check:
36.8698976458 + 53.1301023542 + 90 = 180
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answer:
the acute angles are:
A = 36.8698976458 degrees
B = 53.1301023542 degrees
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