find remaining parts of triangle

Question

In △ABC, m∠A=α, m∠B=β , m∠C=γ. AB=c , AC=b , BC=a. Find the remaining parts of each triangle if the following parts are given. a =45.0, b =26, α =64°.

Answer: c≈ , β≈ °, γ≈ °

Answer 1

Since you are given an interior angle and the side opposite that angle, you can use the Law of Sines

(sin 64)/45 = (sin B)/26 cross multiply and solve to get sinB by itself: (sinB) = 26(sin64)/45 Use inverse sin to get the measure of angle B = 31.28 degrees

To get angle C 180 - (64 + 31.28) = 84.72

Use Law of Sines one more time to find side AB: (sin64)/45 = (sin 84.72)/AB AB = 45(sin84.72)/(sin64) = 49.85