Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠A1 is smaller than ∠A2.) b = 122, c = 163, ∠B = 43°

Answer 1

sin43/122 = sinC/163

sinC = 163sin43/122 = 0.911

C = 65.64 degrees

A = 180-43-65.64 = 180-108.64 = 71.36 degrees

a/sinA = 122/sin43 =

asin43 = 122sinA = 122sin71.36 = 115.6

a = 115.6/sin43 = 169.5

sides are 122, 163 and 169.6

angles are 43, 65.64 and 71.36 degrees

by law of sines

sin43/122 = sin65.64/163 = sin71.36/169.6 = 5.59 x 10^-3 = constant ratio of sines to opposite sides of the triangle

sinB/b = sinC/c= sinA/a

one last thing you might check is to make sure the 3 sides are not impossible

each side cannot be longer than the sum of the other two sides

122<163+169.6

163<122+169.6

169.6 < 122 + 163

also no side can be less than the difference of the other 2 sides

122>169.6-163

169.6 > 163-122

163 > 169.6-122

so, there is no problem. the sides are feasible.