Right triangle & unit circle solver
Solve any right triangle from one angle and one side — or explore the unit circle to see where sin, cos, and tan come from.
Result
Angle A = 30° · Angle B = 60° · Right angle C = 90°
Exact at 30°: sin A = 1/2 · cos A = √3/2 · tan A = √3/3
sin A = 0.5 cos A = 0.866 tan A = 0.5774 | csc = 2 sec = 1.1547 cot = 1.7321
How is this calculated?
In a right triangle with angle A, the three sides are named by their position relative to A: opposite (a) is across from A, adjacent (b) is beside it, and hypotenuse (c) is always opposite the right angle. The three ratios — SOH·CAH·TOA — follow directly: sin A = a/c, cos A = b/c, tan A = a/b. Knowing one angle and one side fixes the entire triangle because the ratios lock in its shape. Know two sides instead? The Pythagorean theorem (a² + b² = c²) gives the third, and the inverse ratios (tan⁻¹, sin⁻¹, cos⁻¹) recover the angle.