Trigonometric Ratios

The sine of an angle A is defined as the ratio of the length of the opposite side to the length of the hypotenuse: $$\text{sin}(A) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

The cosine of an angle A is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: $$\text{cos}(A) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .

The tangent of an angle A is defined as the ratio of the length of the opposite side to the length of the adjacent side: $$\text{tan}(A) = \frac{\text{opposite}}{\text{adjacent}}$$ .

SOH stands for Sine = Opposite over Hypotenuse: $$\text{sin}(A) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

CAH stands for Cosine = Adjacent over Hypotenuse: $$\text{cos}(A) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .

TOA stands for Tangent = Opposite over Adjacent: $$\text{tan}(A) = \frac{\text{opposite}}{\text{adjacent}}$$ .

In a right triangle, the sum of the angles is always 180 degrees, and one angle is always 90 degrees.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: $$c^2 = a^2 + b^2$$ .

To find the missing angle, use the fact that the sum of the angles in a triangle is 180 degrees. If one angle is 90 degrees, subtract the sum of the other two angles from 90.

The sine of a 30° angle is $$\frac{1}{2}$$ .