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

1 Answer
Feb 17, 2018

Answer:

#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#