How this calculator works
Right-triangle trigonometry connects angles to side ratios. First identify the hypotenuse across from the 90° corner. Then, relative to the chosen acute angle, identify the opposite and adjacent legs. The ratio table spells out SOH-CAH-TOA and the three reciprocals. Angle-only mode also accepts angles outside an acute triangle and uses their unit-circle definitions; it does not invent a side length. Triangle modes include area and both acute angles.
Formula
SOH: sin A=a/c; CAH: cos A=b/c; TOA: tan A=a/b. c²=a²+b²; A+B=90°; cot A=b/a; sec A=c/b; csc A=c/a.
Worked example
For opposite leg 3 m and adjacent leg 4 m, c=5 m. The ratios are sin A=3/5, cos A=4/5 and tan A=3/4. With A=30° and c=10 cm, the opposite leg is 5 cm and the adjacent leg is 5√3 cm.
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Frequently asked questions
Does adjacent include the hypotenuse?
In these ratios, adjacent means the leg touching A. The hypotenuse also touches A geometrically, but is named separately.
Why does the chosen angle matter?
Switching to the other acute angle exchanges opposite and adjacent. Sine at one angle becomes cosine at the other.
Can trigonometry be used beyond right triangles?
Yes. Unit-circle functions apply to general angles, and the sine and cosine laws solve oblique triangles. The length-solving modes on this page assume a right triangle.