Answer:
Law of cosines
Step-by-step explanation:
In this problem i need to use the law of cosines, because the angles are unknown.
we know that
The formula of the law of cosines is equal to
[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]
where
[tex]a=7\ units\\b=8\ units\\c=10\ units\\C=\theta[/tex]
substitute in the formula
[tex]10^2=7^2+8^2-2(7)(8)cos(\theta)[/tex]
[tex]100=49+64-112cos(\theta)[/tex]
[tex]100=113-112cos(\theta)[/tex]
[tex]112cos(\theta)=113-100[/tex]
[tex]112cos(\theta)=13[/tex]
[tex]cos(\theta)=\frac{13}{112}[/tex]
using a calculator
[tex]\theta=cos^-1(\frac{13}{112})[/tex]
[tex]\theta=83.33\°[/tex]
