Question

Solve the following triangle. Round all values to the nearest tenth:

a = 30, c = 22, A = 102◦

Answer 1

We can use the Law of Sines (sinA/a=sinB/b=sinC/c)

sinC/22=sin102/30

C=arcsin(22sin102/30)

C≈45.83° (to nearest hundredth of a degree), since A+B+C=180

B≈32.17° (to nearest hundredth of a degree)

sin102/30=sin32.17/b

b=30sin32.17/sin102

b≈16.33 (to nearest hundredth of a unit)

So a,b, and c are 30, 16.33, 22 respectively and:

A,B, and C are 102°, 32.17°, and 45.83° respectively.