Find the indicated angle è.

Question

(Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 110 and c = 136 (angle B=38)
Round your answer to two decimal places.)

Answer 1

Law of Cosines:

cosB = (a^2+c^2-b^2)/2ac.
cos38 = ((110)^2+(136)^2-b^2) / 29920.
0.7880 = (30596-b^2) / 29920.
Cross multiply:
30,596-b^2 = 0.7880*29920 = 23576.96.
-b^2 = 23,976.96-30596 = -6619.04.
b^2 = 6619.04.
b = 81.36.

Law of Sines:

sinA/a = sinB/b.
sinA / 110 = sin38 / 81.36.
Multiply both sides by 110:
sinA = 110(sin38 / 81.36) = 0.832384.
A = 56.34 Deg.

C = 180 - 38 - 56.34 = 85.66 Deg.