Answer:
50°
Step-by-step explanation:
Use the cosine law:
[tex]AB^2=CB^2+CA^2-(CB)(CA)\cos(\angle C)[/tex]
We have:
[tex]AB=6,\ CB=6.5,\ CA=7.5[/tex]
Substitute:
[tex]6^2=6.5^2+7.5^2-2(6.5)(7.5)\cos(\angle C)[/tex]
[tex]36=42.25+56.25-97.5\cos(\angle C)[/tex]
[tex]36=98.5-97.5\cos(\angle C)[/tex] subtract 98.5 from both sides
[tex]-62.5=-97.5\cos(\angle C)[/tex] divide both sides by (-97.5)
[tex]\cos(\angle C)\approx0.641\to m\angle C\approx50^o[/tex]
