Question

Given the triangle below, what is m

Answer 1

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.

$(\text{ the side opposite the angle you want to find })^2=a^2+b^2-2ab \cos(\text{ the angle you want to find})$

Let's enter are values in.

$12^2=10^2+8^2-2(10)(8) \cos(B)$

I'm going to a little simplification like multiplication and exponents.

$144=100+64-160 \cos(B)$

I'm going to some more simplification like addition.

$144=164-160\cos(B)$

Now time for the solving part.

I'm going to subtract 164 on both sides:

$-20=-160\cos(B)$

I'm going to divide both sides by -160:

$\frac{-20}{-160}=\cos(B)$

Simplifying left hand side fraction a little:

$\frac{1}{8}=\cos(B)$

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:

$\cos^{-1}( )$ or $\arccos( )$

Pick your favorite notation there.  They are the same.

$\cos^{-1}(\frac{1}{8})=B$

To the calculator now:

$82.81924422=B$

Round answer to nearest tenths:

$82.8$