Trigonometric Functions and Ratios

A trigonometric function relates the angles of a triangle to the lengths of its sides. The primary trigonometric functions are sine, cosine, and tangent.

Sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: $$\text{sine}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

Cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse: $$\text{cosine}(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .

Tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: $$\text{tangent}(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ .

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides: $$a^2 + b^2 = c^2$$ .

You should use the sine function.

You should use the cosine function.

You should use the tangent function.

Sine and cosine are complementary functions: $$\text{sine}(\theta) = \text{cosine}(90^\text{o} - \theta)$$ .

Use the appropriate trigonometric function based on the known sides and the angle, then rearrange the formula to solve for the unknown side.