Question

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

Answer 1

`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`