Complete the table to show the name of each side of the right triangle when you consider angles a and b

See explanation and table below.

Step-by-step explanation:

There are a few things you need to understand.

A right triangle has one single hypotenuse and two legs. The legs form the right angle. The hypotenuse is opposite the right angle. Since there is a single hypotenuse, the hypotenuse is simply called "hypotenuse" because we always know which side it is.

There are two legs and two acute angles. We need to refer to each leg and to be able to distinguish them, so we call one leg the adjacent leg, and the other leg the opposite leg. The names of the legs, adjacent and opposite, depend on which acute angle you are referring to.

Keep in mind that "adjacent" means "next to" and opposite means "across from".

Look at angle A.

Side "a" is across from angle A, so for angle A, side "a" is "opposite".

Side "b" is next to angle A, so for angle A, side "b" is "adjacent".

Now look at angle B.

Side "a" is next to angle B, so for angle B, side "a" is "adjacent".

Side "b" is across from angle B, so for angle B, side "b" is "opposite".

Side "c" is always the hypotenuse no matter which angle, A or B, you are using.

Table:

                    a                          b                            c

<A           opposite             adjacent             hypotenuse

<B           adjacent              opposite            hypotenuse

3x^3-x^2+6x-9