Sine, Cosine, and Tangent of an Acute Angle in a Right Triangle
Big Idea: Trigonometric ratios allow us to connect angles to side lengths in a right triangle. If you know one acute angle and one side, you can find every other side!
The Right Triangle Setup
Every right triangle has:
- One right angle (90°)
- Two acute angles (each less than 90°)
- Three sides with special names relative to a chosen acute angle
When we pick an acute angle (let's call it $\theta$), the three sides get these names:
- Hypotenuse: The longest side, always opposite the right angle
- Opposite: The side directly across from angle $\theta$
- Adjacent: The side next to angle $\theta$ (that is NOT the hypotenuse)
Interactive visualization — available in the full lesson