How do you solve the triangle given a=21.5, b=13, C=38?

1 Answer
Feb 17, 2018

c=13.8113, B=35.4151^o, A=106.5849^o

Explanation:

We use law of cosines to find side c.
c^2=(21.5)^2+(13)^2-2(21.5)(13)cos(38).
Square rooting both sides, we get c=13.8113.
From there, we can use law of sines to find angle B.
sin(B)/13=sin(38)/9.8673.
Solving, we get sin(B)=(13sin(38))/13.8113.
Using sin^-1, we get sin^-1((13sin(38))/13.8113)=35.4151^o
Subtracting from 180 to find the third angle,we get
A= 180-38-35.4151=106.5849^o