Solve triangle ABC (B= 95°) (C=35°) (b=100 in)

Question

Round answers to the nearest tenth.

Answer 1

sum of 3 angles of a any triangle always = 180

A+B+C = 180

A = 180-B-C = 180-95-35 = 180 -130 = 50 degrees

A = 50

Use the Law of Sines. ratio of a side to its opposite angle is a constant

c/sinC = b/sinB = a/sinA

b/sinB = 100/sin95 = 100.382

c/sin35 = 100.382

c =100.382sin35 = 57.577675= about 57.6

c= 57.6

a/sinA = a/sin50 = 100.382

a = 100.382sin50 = 76.9

a = 76.9

sides are a, b and c = 76.9, 100, and 57.6 inches

angles are A, B, and C = 50, 95, and 35 degrees

longest side is opposite the largest angle, 100 inches is opposite 95 degrees

smallest side is opposite the smallest angle 57.6 inches is opposite 35 degrees

check the answer, using the Law of Cosines

c^2 = a^2 + b^2 - 2abCosC

57.6^2 = 76.9^2 + 100^2 - 2(76.9)(100)Cos35

3,317.8 = 5,913.6 +10,000 - 15380Cos35

3317.8 = 15,913.6 -12,598.6

3318 is close to 3315. maybe some rounding errors somewhere compounded

sketch a rough graph might help