Iam confused with the pythagorean theorem

Let me help you do a few.

Trigonometry helps you find missing side lengths through an angle, one given side length, and a given function. We can use trig ratios and functions to figure this out.

Remember Chief S o/h C a/h T o/a

Where o is the opposite side of the given angle, h is the hypotenuse, and a is the adjacent side of the given angle. S= sine C= cosine and T= tangent

For the first one, 

You have the angle 27. You have the measure of the adjacent side (10) and you are trying to figure out the measure of the opposite side x. (0)

We will use T (tangent) because it has the adjacent and opposite side to help us solve. T o/a

(Tangent 27)= x/10 

Multiply 10 to the other side.

(Tangent 27)*10= x

Plug into a calculator. 

x=17.505... 17.5 at the nearest tenth.

One more.

Same deal, we have the measure of the angle and we are trying to find the opposite side. We will use tangent again.

Tan 25= x/10
Multiply 10 to the other side.

Tan 25*10=x
x=16.209... 16.2

Note: when I used the google calculator, you enter the side length in the parenthesis after you choose Sin, Cos, or Tan. Then you multiply by the measure of the angle. Sometimes the way you do it for the answer varies. If you get a negative number, you probably entered it in wrong.

I hope this helps! Let me know if you have any more questions.
~kaikers

The correct answer will be d. -4