Calculate the opposite side, adjacent side and tangent in a right triangle, from an angle and the hypotenuse.
In a right triangle, the trigonometric functions describe the ratio between the sides and one of the acute angles:
The calculator rearranges the sine and cosine formulas to find the sides: opposite = hypotenuse × sin(a) and adjacent = hypotenuse × cos(a).
A common mnemonic for which side belongs to which function is SOH-CAH-TOA: Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent.
SOH-CAH-TOA is a mnemonic for the three basic trigonometric ratios: Sine = Opposite ÷ Hypotenuse (SOH), Cosine = Adjacent ÷ Hypotenuse (CAH), Tangent = Opposite ÷ Adjacent (TOA).
All three describe the ratio between two sides of a right triangle, seen from a given angle. Sine uses the opposite and hypotenuse, cosine uses the adjacent and hypotenuse, while tangent uses the opposite and adjacent (and therefore doesn't need the hypotenuse).
No, these formulas only apply to right triangles. For arbitrary triangles, you need to use the law of sines or the law of cosines instead.