Question

TRIGONOMETRY PLEASE !!!

Answer 1

`45.6=x`

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:

`(-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`