Trigonometric Ratios

Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse. Formula: sin(θ) = Opp/Hyp.

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: cos(θ) = Adj/Hyp.

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side. Formula: tan(θ) = Opp/Adj.

Soh Cah Toa: Sine = Opp/Hyp, Cosine = Adj/Hyp, Tangent = Opp/Adj.

sin(θ) = Opp/Hyp = 8/10 = 0.8.

cos(θ) = Adj/Hyp = 6/10 = 0.6.

tan(θ) = Opp/Adj = 4/3.

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Formula: a² + b² = c².

Using the Pythagorean theorem: 3² + b² = 5²; b² = 25 - 9; b = 4.

sin(30°) = 1/2.