The law of cosines can be written as:
[tex]p^2=a^2+b^2-2\text{abCosP}[/tex]
Where
p, a, and b are the sides
P is the angle opposite of side p
Now,
x is what we want to find and other two sides given are 25 and 50 (let them be a and b)
Angle opposite to side unknown is 39 degrees, this is Angle P
Substituting, we get:
[tex]\begin{gathered} p^2=a^2+b^2-2\text{abCosP} \\ x^2=25^2+50^2-2(25)(50)\text{Cos}39 \\ x^2=3125-2500Cos39 \\ x^2=3125-1942.86 \\ x=\sqrt[]{3125-1942.86} \\ x=34.38 \end{gathered}[/tex]
