Pythagoras' Theorem

c is always the hypotenuse (the longest side).

Formula: a² + b² = c²

Example: Sides 3 and 4: 3² + 4² = 25. √25 = 5.

Finding a Shorter Side

Subtract the squares: c² - a² = b².

Example: Hyp=13, side=5: 169 - 25 = 144. √144 = 12.

Trigonometry (SOH CAH TOA)

Links angles and sides. Label sides: Opposite (from angle), Adjacent (next to), Hypotenuse (longest).

Formula: sin θ = O/H, cos θ = A/H, tan θ = O/A

Finding a Length

Pick Sin, Cos, or Tan based on what you have and what you want. Rearrange the formula.

Finding an Angle

Use the inverse trig buttons (sin⁻¹, cos⁻¹, tan⁻¹).

Example: sin θ = 0.5 → θ = sin⁻¹(0.5) = 30°

Pythagoras in 3D

Apply a² + b² + c² = d² to find diagonals across rooms or pyramids.

Example: Box 3x4x12: √(3²+4²+12²) = √169 = 13.

Exact Trig Values

You must memorize sin/cos/tan for 0, 30, 45, 60, 90.

Trig Graphs

Know the shapes of Sine, Cosine, and Tangent waves from 0° to 360°.