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.

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 =63.8, β =58.5º, γ =22.0º

b≈ , c≈ , α = °

Answer 1

Because we have 2 angles and one side measure, the other dimensions of the triangle are determined (that is, this is not an ambiguous case).

Use the fact that the interior angles sum to 180° to get α. Then, law of sines is easy to get the other 2 sides since we have a side-angle pair:

63.8 / sinα = b / sin58.5° etc.