What does SOH-CAH-TOA stand for?
It is a memory aid for the three ratios: Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, and Tangent = Opposite ÷ Adjacent, all taken with respect to one acute angle.
// maths › Foundations
Intro to sin, cos, tan
Learn the three trigonometric ratios sine, cosine, and tangent from the sides of a right triangle using SOH-CAH-TOA, with a diagram that labels the opposite, adjacent, and hypotenuse and highlights which two sides each ratio uses.
sin = O/H · cos = A/H · tan = O/A (SOH-CAH-TOA)
Frequently asked questions
How do I know which side is opposite or adjacent?
Stand at the angle you care about. The hypotenuse is always opposite the right angle (the longest side). The opposite side is across from your angle, and the adjacent side is the remaining one beside it.
Can you give a worked example?
In a 3-4-5 right triangle with opposite = 3, adjacent = 4 and hypotenuse = 5: sine = 3/5 = 0.6, cosine = 4/5 = 0.8, and tangent = 3/4 = 0.75.
Why do the ratios stay the same for any size triangle?
All right triangles with the same acute angle are similar, so their side ratios are identical regardless of size. That is why each ratio depends only on the angle.
Where is this used in real life?
Surveyors and builders find heights and distances, engineers resolve forces into components, sailors and pilots navigate, sound and music engineers model waves, and game developers compute movement and lighting angles.