Finding Side Lengths Using Trig

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side.

SOH CAH TOA is a mnemonic to remember the definitions of sine, cosine, and tangent: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

To set up a cosine ratio, use the formula: $$\text{cos}(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .

You can find the adjacent side by rearranging the cosine formula: $$\text{adjacent} = \text{hypotenuse} \times \text{cos}(\theta)$$ .

The cosine of 37 degrees is approximately 0.7986.

To set up a sine ratio, use the formula: $$\text{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

You can find the opposite side by rearranging the sine formula: $$\text{opposite} = \text{hypotenuse} \times \text{sin}(\theta)$$ .

The sine of 37 degrees is approximately 0.6018.