Finding Missing Sides and Angles Right Triangle Trig Review

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$c^2 = a^2 + b^2$$ .

The sine ratio is defined as the ratio of the length of the opposite side (O) to the length of the hypotenuse (H). It can be expressed as: $$\text{sine} = \frac{O}{H}$$ .

The cosine ratio is defined as the ratio of the length of the adjacent side (A) to the length of the hypotenuse (H). It can be expressed as: $$\text{cosine} = \frac{A}{H}$$ .

The tangent ratio is defined as the ratio of the length of the opposite side (O) to the length of the adjacent side (A). It can be expressed as: $$\text{tangent} = \frac{O}{A}$$ .

To find a missing side in a right triangle, you can use the Pythagorean theorem or trigonometric ratios (sine, cosine, tangent) depending on the information given.

Degrees and radians are two units for measuring angles. 180 degrees is equal to $$\frac{\text{π}}{1}$$ radians.

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

You should use a calculator in degree mode when you are working with angles measured in degrees, especially in trigonometric calculations.

To find the hypotenuse (H) using sine, you can rearrange the sine ratio: $$H = \frac{O}{\text{sine}}$$ .

To find the adjacent side (A) using cosine, you can rearrange the cosine ratio: $$A = H \times \text{cosine}$$ .