Question

suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120 degrees. what is the length of the third side of the triangle?

Answer 1

Use the law of cosines
\[

c^2 = a^2 + b^2 - 2 a b \cos(\theta)

\]

Answer 2

\[c^2 = 32^2 + 35^2 - 2(32)(35) \cos(120)\]

Answer 3

\[
c^2= 1024 + 1225 -2240\left(-\frac 1 2 \right)=3369\\
c=\sqrt{3369}\approx 58.04
\]

Answer 4

I don't quite understand the steps but it makes sorta sense