SOLUTION: if the perimeter of the triangle ABC equals 12cm , m(<A)=47, and m(<B)=53, find the lenght of AB to the nearest cm ....

Algebra ->  Trigonometry-basics -> SOLUTION: if the perimeter of the triangle ABC equals 12cm , m(<A)=47, and m(<B)=53, find the lenght of AB to the nearest cm ....       Log On


   

Question 327985: if the perimeter of the triangle ABC equals 12cm , m(
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since A%2BB=100 then C=80
since A%2BB%2BC=180
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From the law of sines,
BC%2Fsin%28A%29=AC%2Fsin%28B%29=AB%2Fsin%28C%29
BC%2Fsin%2847%29=AC%2Fsin%2853%29=AB%2Fsin%2880%29
From the perimeter,
AB%2BBC%2BAC=12
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From the law of sines equation,
BC=AB%2A%28sin%2847%29%2Fsin%2880%29%29
AC=AB%2A%28sin%2852%29%2Fsin%2880%29%29
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Substituting into the perimeter equation,
AB%2BAB%28sin%2847%29%2Fsin%2880%29%29%2BAB%28sin%2853%29%2Fsin%2880%29%29=12
AB%2A%281%2Bsin%2847%29%2Fsin%2880%29%2Bsin%2853%29%2Fsin%2880%29%29=12
AB%281%2B0.7426%2B0.8110%29=12
AB=12%2F2.554
AB=4.699
To the nearest cm,
AB=5cm