Given: a=5
b=12
angle C =90 degrees
We have to find c using law of cosines.
The law of cosines is given by:
[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]Putting the values,we have:
[tex]\begin{gathered} c^2=5^2+12^2-2\times5\times12\times\cos (90^{\circ}) \\ =25+144-0 \end{gathered}[/tex][tex]c^2=169[/tex]Taking squareroot we get :c=13 0r c=-13
But the side length can be a positive number so c=13.
The answer is c=13.
