Warm Up
The Pythagorean Theorem is a relationship between the three sides of a right triangle. This relationship is often written 
, where c is the length of the hypotenuse and the lengths of the other two sides are a and b.
Example 1
Determine the length of the unknown side of the triangle.
The triangle has a right angle so the Pythagorean Theorem can be used.
The cosine ratio describes the relationship between two sides of a right triangle. The cosine of an acute angle in a right triangle is the ratio of the side adjacent to that angle to the hypotenuse.
Two cosine ratios for the same triangle are shown below.
Sometimes the cosine ratio is written as 
or 
.
The tangent ratio is the third trigonometric ratio you are familiar with. The tangent ratio describes the relationship between two sides of a right triangle as well. The tangent of an acute angle in a right triangle is equal to the ratio of the side opposite that angle to the non-hypotenuse side that is adjacent to the angle.
Two tangent ratios for the same triangle are shown below.
