Solve a right triangle given any two known values — two sides, or one side and one acute angle. Find all missing sides and angles, see trig ratios, and get a labeled diagram.
| Angle | sin | cos | tan |
|---|---|---|---|
| A | — | — | — |
| B | — | — | — |
sin A = opposite / hypotenuse = a / c
cos A = adjacent / hypotenuse = b / c
tan A = opposite / adjacent = a / b
SOH-CAH-TOA is a mnemonic for the three primary trig functions in a right triangle. For angle A, the opposite side is a, the adjacent side is b, and the hypotenuse is c.
To solve for an unknown side from two knowns, rearrange: e.g., a = c · sin A. To find a missing angle, use the inverse functions: A = arcsin(a/c).
a² + b² = c²
In every right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. This lets us find the third side whenever two sides are known.
The Pythagorean theorem and SOH-CAH-TOA work together: once you have all three sides, you can compute all six trig ratios. Once you have an angle and a side, the trig functions give you the remaining sides directly.
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