Question

In △ABC, m∠A = α, m∠B = β, m∠C = γ. AB = c, AC = b, BC = a. . Find the angles of the triangle knowing that the sides of the triangle are: a=39.5, b=45.2, c=67.1

Answer 1

Answer:

m < A =   34.44 degrees.

m < B =   40.60 degrees.

m < C = 104.96 degrees.

Step-by-step explanation:

Using the Cosine Rule we have;

c^2 = a^2 + b^2 - 2ab cos C

67.1^2 = 45.2^2 + 39.5^2 - 2*39.5*45.2 cos C

cos C =  (67.1^2 - 45.2^2 - 39.5^2) / (-2*39.5*45.2)

cos C = -0.25841

C = 104.96 degrees

Using the Sine Rule:

c / sin C = b / sin B

67.1/ sin 104.96 = 45.2 / sin B

sin B = (45.2 * sin 104.96) / 67.1

= 0.65079

B = 40.60 degrees.

So A = 180 - 40.60 - 104.96 = 34.44 degrees.