Solve triangle ABC if a = 20, b = 30, c = 22

Question

∠A= __°

 

∠B=___° 

 

∠C=___°

 

Answer 1

Use the Law of Cosines to first find the largest angle.  The largest angle is opposite the largest side, namely side b.

 

b² = a² + c² - 2accosB

 

900 = 400 + 484 - 880cosB

 

cosB = -0.01818

 

∠B = cos^-1(-0.01818) ≈ 91.0°

 

Use the Law of Sines to find either one of the other 2 sides:

 

sin(91.0°)/30 = sinC/22

 

sinC = 0.73322

 

∠C = Sin^-1(0.73322) ≈ 47.2°

 

So, ∠A = 180° - ∠B - ∠C ≈ 41.8°

 

Answer 2

Use law of cosine to find one of the angles, since we know all the sides.

 

c² = a² + b² - 2abCosC

484 = 400 + 900 - 1200CosC

484 = 1300 - 1200CosC

-816 = -1200CosC

0.68 = CosC

47.156 = C

 

b² = a² + c² - 2acCosB

600 = 400 + 484 - 880CosB

600 = 884 - 880CosB

-284 = -880CosB

0.323 = CosB

71.156 = B

 

 

A = 180 - B - C