Use the Law of Sines to solve the triangles. A = 56°, a = 12, b = 14

Answer 1

Angle A = 56, side a = 12 and side b = 14.

By the Law of Sines in the reciprocal form

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

sin(B) = b * [sin(A) / a]

Substitute the values of A = 56, a = 12 and b = 14

sin(B) = (14) * [sin(56) / 12] = (7/6) * sin(56) = (1.16667) * (0.829) = 0.9672.

B =  sin ^-1(0.9672) = 75.29⁰.

 

The sum of three angle in a triangle is 180.

A + B +C = 180

C = 180 - (A + B ) = 180 - (56 + 75.29 ) = 180 - 131.29 = 48.71.

 

The remaining side is

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

c = [a/sin(A)] * sin(C)

c = [12/sin(56)] * sin(48.71) = [12 / (0.829)] * (0.7514) = 10.88 units.

Angles B = 75.29⁰, C = 48.71⁰ and side c = 10.88.