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Solution to Problem: 
We are given angle A and the side opposite to it with c the hypotenuse. The sine ratio gives a relationship between the angle, the side opposite to it and the hypotenuse as follows 
sin A = opposite / hypotenuse 
Angle A and opposite side are known, hence 
sin 31 ^o = 5.12 / c 
Solve for c 
c = 5.12 / sin 31 ^o
and use a calculator to obtain 
c (approximately) = 9.94