Today I am going to show you how to solve Trigonometric Ratios. "Trigon" is Greek for triangle, and "metric" is Greek for measurement. The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring 90 degrees). Remember that the two sides of a right triangle which form the right angle are called the legs, and the third side (opposite the right angle) is called the hypotenuse.

## Step 1: Trigonometric Ratios

A **trigonometric ratio** is a ratio of two sides of a right triangle. There are three basic trigonometric ratios: **sine, cosine, and tangent**. Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non-90o angles. Here is an Example: The triangle is in the image.

Write expressions for the sine, cosine, and tangent of A.

The length of the leg opposite A is a. The length of the leg adjacent to A is b, and the length of the hypotenuse is c.

The sine of the angle is given by the ratio "opposite over hypotenuse." So,

The cosine is given by the ratio "adjacent over hypotenuse."

The tangent is given by the ratio "opposite over adjacent."

Generations of students have used the mnemonic "SOHCAHTOA" to remember which ratio is which. (Sine: Opposite over Hypotenuse, Cosine: Adjacent over Hypotenuse, Tangent: Opposite over Adjacent.)