Question

TRIGONOMETRY PLEASE !!!

Answer 1

Answer:

$45.6=x$

Step-by-step explanation:

We can use law of cosines since three sides are given and we are asked to find an angle.

$c^2=a^2+b^2-2ab\cos(C)$

Angle $C$ is the angle that is opposite to the side $c$.

So here $x$ is our Angle $C$ and the side opposite to that is 11 which makes it $c$ for this formula.

This means $a=8$ and $b=15$ (or other way around-doesn't matter).

Let's plug in:

$11^2=8^2+15^2-2(8)(15)\cos(x)$

Simplify the terms with exponents:

$121=64+225-2(8)(15)\cos(x)$

Perform the multiplication next to the trig function:

$121=64+225-240\cos(x)$

Add 64 and 225:

$121=289-240\cos(x)$

Our goal is to isolate the trig function.

Subtract 289 on both sides:

$121-289=-240\cos(x)$

Simplify left hand side:

$-168=-240\cos(x)$

Divide both sides by -240:

$\frac{-168}{-240}=\cos(x)$

Simplify left hand side:

$0.7=\cos(x)$

Take cosine's inverse on both side:

$\cos^{-1}(0.7)=x$

Type left hand side into calculator:

$45.6=x$