Answer:
82.8 degrees
Step-by-step explanation:
The information given here SSS. That means side-side-side.
So we get to use law of cosines.
[tex](\text{ the side opposite the angle you want to find })^2=a^2+b^2-2ab \cos(\text{ the angle you want to find})[/tex]
Let's enter are values in.
[tex]12^2=10^2+8^2-2(10)(8) \cos(B)[/tex]
I'm going to a little simplification like multiplication and exponents.
[tex]144=100+64-160 \cos(B)[/tex]
I'm going to some more simplification like addition.
[tex]144=164-160\cos(B)[/tex]
Now time for the solving part.
I'm going to subtract 164 on both sides:
[tex]-20=-160\cos(B)[/tex]
I'm going to divide both sides by -160:
[tex]\frac{-20}{-160}=\cos(B)[/tex]
Simplifying left hand side fraction a little:
[tex]\frac{1}{8}=\cos(B)[/tex]
Now to find B since it is inside the cosine, we just have to do the inverse of cosine.
That looks like one of these:
[tex]\cos^{-1}( )[/tex] or [tex]\arccos( )[/tex]
Pick your favorite notation there. They are the same.
[tex]\cos^{-1}(\frac{1}{8})=B[/tex]
To the calculator now:
[tex]82.81924422=B[/tex]
Round answer to nearest tenths:
[tex]82.8[/tex]
