Final answer:
To solve the triangle, we can use the Law of Cosines to find the missing side length and then use the Law of Sines to find angle C. Substituting the given values into the equations, we find that angle C is approximately 30.1°.
Step-by-step explanation:
To solve the triangle, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and the angle A opposite side a, the following equation holds true: c^2 = a^2 + b^2 - 2ab * cos(C)
Substituting the given values, we get:
70^2 = 54^2 + b^2 - 2 * 54 * b * cos(106)
Simplifying and solving for b, we find that b ≈ 37.64.
Now we can use the Law of Sines to find the value of angle C. This can be done using the following equation: sin(C) / c = sin(B) / b
Substituting the given values, we get:
sin(C) / 70 = sin(106) / 37.64
Simplifying and solving for sin(C), we find that sin(C) ≈ 0.509.
Taking the arcsin of 0.509, we find that angle C ≈ 30.1°.