Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 56°, a = 12, b = 14
1 answer:
We know thatcase 1) Applying the law of sines a/Sin A=b/Sin B A=56° a=12 b=14 so a*Sin B=b*Sin A----> Sin B=b*Sin A/a---> Sin B=14*Sin 56°/12 Sin B=0.9672 B=arc sin (0.9672)------> B=75.29°-----> B=75.3° find angle C A+B+C=180°-----> C=180-(A+B)----> C=180-(56+75.3)----> C=48.7° find c a/Sin A=c/Sin C----> c=a*Sin C/Sin A----> c=12*Sin 48.7°/Sin 56°) c=10.87-----> c=10.9the answer Part 1) the dimensions of the triangle N 1 are a=12 A=56° b=14 B=75.3° c=10.9 C=48.7° case 2) A=56° a=12 b=14 B=180-75.3----> B=104.7° find angle C A+B+C=180°-----> C=180-(A+B)----> C=180-(56+104.7)----> C=19.3° find c a/Sin A=c/Sin C----> c=a*Sin C/Sin A----> c=12*Sin 19.3°/Sin 56°) c=4.78-----> c=4.8the answer Part 2) the dimensions of the triangle N 2 are a=12 A=56° b=14 B=104.7° c=4.8 C=19.3°
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