How do you solve the triangle when a=3, b=2, A=50degrees?

1 Answer
Jun 23, 2017

hatB~=30.71°; hat C~=99.29°; c~=3.86

Explanation:

Since, by the sine theorem, it's

a/sin hatA=b/sin hatB

you get

3/(sin50°)=2/sin hatB

then

sin hatB=2/3sin 50°~=0.51

and hatB~=30.71°

Then, since the sum of the angles is 180°, you get

hat C=180°-50-30.71~=99.29°

and you would apply the sine theorem again to find c:

a/sin hatA=c/sin hatC

3/(sin50°)=c/(sin 99.29°)

that's

c=3(sin99.29°)/(sin50°)~=3.86