Question

I don't Understand Trig.

Answer 1

I'll give you a brief explanation of the tangent ratio.
A right triangle has one right angle and 2 acute angles.
The right angle is opposite the longest side of the triangle. That side is called the hypotenuse.

The other two sides are the sides that form the right angle. They are called legs. The two legs may or may not have the same length, but the hypotenuse is always longer than either one of the legs.

The tangent ratio of trigonometry is the ratio of the lengths of the two legs.
It is a specific ratio using the legs in a specific order.

The tangent of an acute angle of a triangle is the ratio of the length of the opposite leg to the length of the adjacent leg.

I will use your triangle to explain the ratio.

Triangle XYZ has right angle Y.
The two acute angles are X and Z.
Triangle XYZ has a hypotenuse, side XZ, opposite the right angle.
Triangle XYZ has two legs, sides XY and YZ.

Since there is only one hypotenuse, if you mention the hypotenuse, you automatically know which side we are talking about. Since there are two legs, if I just mention "leg", you don't know which specific leg I mean. In order to know which specific leg I mean, I need to specify more. The legs are called adjacent leg and opposite leg. These terms are based on one of the acute angles.

The problem asks for the value of tan Z.
Z is one of the acute angles.
For angle Z, the adjacent leg is side YZ. Adjacent means "next to." The only leg next to angle Z is leg YZ.
For angle Z, XY is the opposite leg. Opposite means "across from." Leg XY is opposite angle Z.

Here is something you must memorize about the tangent ratio.

tan Z = (opp leg)/(adj leg)

The tangent is the ratio of the length of the opposite leg to the length of the adjacent leg.

tan Z = opp/adj

tan Z = 35/12

Answer: First choice.