Move the slider to change angle θ in a right triangle. Watch the three side lengths update in real time, and see how their ratios — sine (sin), cosine (cos), and tangent (tan) — change along with them.
In a right triangle, relative to angle θ: the side across from θ is called the opposite side, the side touching θ (other than the hypotenuse) is the adjacent side, and the longest side, across from the right angle, is the hypotenuse.
sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent. Even as the triangle's size changes, these ratios stay exactly the same as long as angle θ stays the same — that's why they're called "trig ratios."
Below, pick one of the hypotenuse, adjacent side, or opposite side and type in its length. That side's length stays fixed, and the other two sides are calculated automatically to match the angle.