SOLUTION: PLease help me Find the measure of angle A in Triangle ABC to the nearest degree if A= 4, B= 13, and C= 45 degrees?

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Question 1008804: PLease help me Find the measure of angle A in Triangle ABC to the nearest degree if A= 4, B= 13, and C= 45 degrees?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that a=4 and b=13 are measures of the sides.
Use the law of cosines to find the unknown side, c.
c%5E2=a%5E2%2Bb%5E2-2ab%2Acos%28C%29
c%5E2=4%5E2%2B13%5E2-2%284%29%2813%29%2Acos%2845%29
c%5E2=16%2B169-104%2A%28sqrt%282%29%2F2%29
c%5E2=111.461
c=10.56
Then use the law of sines,
a%2Fsin%28A%29=c%2Fsin%28C%29
4%2Fsin%28A%29=10.56%2Fsin%2845%29
sin%28A%29=%284%2Asin%2845%29%29%2F10.56
sin%28A%29=0.2679
A=15.5