Every right triangle is governed by two things: the Pythagorean theorem (a² + b² = c², relating the two legs to the hypotenuse) and SOH-CAH-TOA (sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent, relating an angle to the side ratios). Between the two, knowing any two values — two sides, or one side and one angle — is enough to solve for everything else.
A ladder leaning against a wall, 5 m long, with its base 3 m from the wall, reaches 4 m up the wall (3-4-5) — and makes an angle of 36.87° with the ground, since sin⁻¹(3/5) = 36.87°.
A point moving around a circle of radius 1 has coordinates (cos θ, sin θ) by definition — the triangle formed by that point, the centre, and the x-axis is a right triangle with hypotenuse 1, so "opposite over hypotenuse" is just the y-coordinate, and "adjacent over hypotenuse" is just the x-coordinate.
It's the same rotation, just unwrapped — plot the circle's y-coordinate against the angle travelled instead of against the x-coordinate, and the smooth up-down oscillation of a wave is exactly what falls out. This is literally how the wave gets traced in the animation above.
A set of three whole numbers that satisfy a² + b² = c² exactly — 3-4-5 is the smallest and most famous, but there are infinitely many (5-12-13, 8-15-17, 7-24-25...), and any multiple of a triple (6-8-10, 9-12-15) is also a valid triple.
Not directly — a general triangle needs the Law of Sines or Law of Cosines instead, since SOH-CAH-TOA and a²+b²=c² both specifically rely on one angle being exactly 90°.
A right triangle in a flat plane, with one angle exactly 90 degrees — the side ratios here do not hold otherwise. Results carry ordinary floating-point rounding, so an exact value like sin 60° = √3⁄2 displays as 0.8660254; that is a display artefact, not an error in the maths. Angles are read in whichever unit you have selected, which is the single most common source of a wrong answer here.
Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.