Notice the 53° angle on the far right side of the same row. This is the other angle in the 3-4-5 triangle and is called the **complementary angle.** A complementary angle is found by subtracting the reference angle from 90° (90° - 37° = **53° **).
Since the reference and complementary angles are in the same triangle, both
angles use the same numbers (length of sides) to derive their functions. The sine of the reference angle is equal to the cosine of the complementary angle, and vice versa.

The following charts show which functions of the reference and the complementary angles are equal to each other.

Notice that any two functions

opposite each other are

identified by a name and

its **co**name.

**Note:** If you name

the sides incorrectly, you will

end up with the complementary

angle instead of the reference angle.

One way to avoid this error is to

remember that the shortest side

is always opposite the smallest

angle.

To solve any math problem, it is necessary to know a certain amount of information. The information given in this book, referred to as **knowns**, is enough information to begin solving the problem presented; however, you may need to add to those knowns by further calculations to arrive at the final answer. The **needs** are the information you are trying to find.

Here is a problem which uses the table to find the angles.

**Find the angles of this triangle.**

**First:** Draw a thumbnail sketch, then label the reference angle and name the sides.

**Adjacent side = 16'****
Opposite side = 8'**

**Second:** Choose the function that uses

the **knowns** to determine the **needs**.

Replace the ratio with the **knowns** and

calculate the problem.
There are two functions which can be

used when you know just the opposite

and adjacent sides: tangent or cotangent.

**Cotangent** is used this time.

**Third:** Refer to the function table to determine the angle.
Look at the functions table on pages 214 and 215 under cot for 2. The closest angle is 26.5° , or **26 1/2° **.

The complementary angle is 90° - 26.5° = 63.5° , or **63 1/2° **. Did you notice the complementary angle on the right side of the table?