Finding Missing Sides and Angles Right Triangle Trig Review

The ratio for Sine is $$\frac{O}{H}$$ , where O is the length of the opposite side and H is the length of the hypotenuse.

The ratio for Cosine is $$\frac{A}{H}$$ , where A is the length of the adjacent side and H is the length of the hypotenuse.

The ratio for Tangent is $$\frac{O}{A}$$ , where O is the length of the opposite side and A is the length of the adjacent side.

SOH CAH TOA is a mnemonic to remember trigonometric ratios: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

To find the missing side, use the appropriate trigonometric ratio (Sine, Cosine, or Tangent) based on the known angles and sides.

The Sine of the angle is $$\frac{3}{5}$$ .

The Cosine of the angle is $$\frac{4}{5}$$ .

The Tangent of the angle is $$\frac{3}{4}$$ .

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

To calculate the angle, use the inverse functions: $$\sin^{-1}(x)$$ for Sine, $$\cos^{-1}(x)$$ for Cosine, and $$\tan^{-1}(x)$$ for Tangent.