Solve the triangle. A = 46°, a = 31, b = 27

A=46 degrees, B=33.4 degrees, C=100.6 degrees

a=34, b=27, c=48.2

Step-by-step explanation:

(a/sin(A)) = (b/sin(B)) = (c/sin(C))

we are given

(34/sin(46)) = (27/sin(B))

34sin(B) = 26sin(46)

34sin(B) = 18.702834809

sin(B) = 0.550083377

note use inverse sin function to find angle B

B = 33.372733167 approx 33.4 degrees then

C = 180 - (46 + 33.4) = 100.6

Then, (b/sin(B)) = (c/sin(C))

27/0.550083377 = c/0.982935349

0.550083377 * c = 27 * 0.982935349

0.550083377 * c = 26.539254427

c = 48.245876056 approx 48.2 .

Lastly, you get: A=46 degrees, B=33.4 degrees, C=100.6 degrees

a=34, b=27, c=48.2

both equations and proportions are better.