Calculate sine, cosine, and tangent ratios for a right triangle from side lengths or find missing sides from an angle.
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How to use
Choose a mode: enter an angle with one side to find the other sides, or enter two sides to find the angle. Uses the SOH-CAH-TOA trig ratios for right triangles.
Also in Triangles
Trigonometry
The SOHCAHTOA calculator finds sine, cosine, and tangent ratios for a right triangle from its side lengths, or finds missing sides when given an angle and one side. SOHCAHTOA is a mnemonic for the three basic trigonometric ratios.
SOHCAHTOA stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent. These three ratios relate an acute angle in a right triangle to the lengths of the sides around it.
sin(theta) = opposite / hypotenuse
SOH — Sine is Opposite over Hypotenuse.
cos(theta) = adjacent / hypotenuse
CAH — Cosine is Adjacent over Hypotenuse.
tan(theta) = opposite / adjacent
TOA — Tangent is Opposite over Adjacent.
If you know one acute angle and one side, rearrange the appropriate ratio to solve for the missing side. For example, if you know the angle and the hypotenuse, the opposite side is hypotenuse times sine of the angle.
If you know two sides, divide them in the correct order to get the ratio, then use the inverse trig function. For instance, if you know the opposite and adjacent sides, the angle is arctan(opposite / adjacent).
Frequently asked questions
No. SOHCAHTOA defines ratios for right triangles only. For other triangles, use the law of sines or the law of cosines.
Identify which two of the three sides (opposite, adjacent, hypotenuse) are involved — that determines whether to use sine, cosine, or tangent.
SOH = Sine is Opposite over Hypotenuse, CAH = Cosine is Adjacent over Hypotenuse, TOA = Tangent is Opposite over Adjacent.
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