Solve ΔABC. (Round your answers to the nearest degree. If there is no solution, enter NO SOLUTION.)

Question

Solve ΔABC. (Round your answers to the nearest degree. If there is no solution, enter NO SOLUTION.)

a = 10,    b = 14,    c = 12

𝛼 =	°
𝛽 =	°
𝛾 =	°

Answer 1

Since 3 sides are given, use the Law of Cosines to find the largest angle (which is opposite the longest side) first

Find β: b² = a² + c² - 2accosβ

196 = 100 + 144 - 2(10)(12)cosβ

196 = 244 - 240cosβ

cosβ = 0.2

β = Cos^-1(0.2) = 78°

Now, use the Law of Sines to find one of the other angles and then use the fact that the 3 angle measures add up to 180° to get the remaining angle.