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. c=4380, α=37º, β=34º

Answer 1

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. c=4380, α=37º, β=34º

I typically set these up by creating the following structure:

A = a =

B = b =

C = c =

Then I fill in all the values that I know at the beginning. This can include any third angle that I can get by the Triangle Angle Sum Theorem.

A = 37° a =

B = 34° b =

C = 109° c = 4380

This allows me to see very clearly that an angle and its opposite side are known, and therefore the Law of Sines can be used. I can get a by the proportion equation ^a/_{sin A} = ^c/_{sin C}, and b by the proportion ^b/_{sin B} = ^c/_{sin C}.

^a/_{sin 37°} = ⁴³⁸⁰/_{sin 109°}

a sin 109° = 4380 sin 37°

a = ^{4380 sin 37°}/_{sin 109°} ≈ 2787.8

^b/_{sin 34°} = ⁴³⁸⁰/_{sin 109°}

b sin 109° = 4380 sin 34°

b = ^{4380 sin 34°}/_{sin 109°} ≈ 2590.4