Trig Calculator — Right Triangle & Sine/Cosine Rule Solver
Enter any two parts of a right triangle — two sides, or a side and an angle — and it solves the rest and draws the triangle to scale as you type, with every side and angle labelled. The second tab handles any triangle by the sine and cosine rules. Sohcahtoa on tap, with the working shown so you can see exactly where each number came from.
Fill in any two boxes (at least one must be a side). Enter more and it uses the two you edited most recently, so you can keep changing your mind and watch the triangle move. Right angle is at C.
Fill in any three boxes, at least one a side (SSS, SAS, ASA, AAS or the ambiguous SSA). Each angle sits opposite the side of the same letter.
Sohcahtoa, and solving triangles on the shop floor
Every right-triangle problem reduces to three ratios, and the mnemonic that carries them is SOH-CAH-TOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent. Fix any two parts of the triangle — two sides, or one side and one of the acute angles — and those three ratios plus Pythagoras (c² = a² + b²) and the fact that the acute angles add to 90° are enough to recover everything else. That is exactly what the right-triangle tab does, and it shows you which ratio it used so the result is auditable rather than magic.
This comes up constantly in a machine shop. The depth to sink a chamfer of a given angle and width; the rise over a run when you set a part on an angle plate; the true length of a hypotenuse feature from its X and Y; the offset to move a tailstock to turn a taper — all of them are a right triangle with two knowns. Working it the wrong way round, or reaching for the calculator app and fat-fingering a ratio, is a classic way to scrap a setup, which is the whole reason for showing the working.
The second tab handles the triangles that are not right-angled, using the two rules that generalise sohcahtoa. The sine rule, a ÷ sin A = b ÷ sin B = c ÷ sin C, solves a triangle when you know two angles and a side, or two sides and a non-included angle. The cosine rule, c² = a² + b² − 2ab·cos C, takes over when you know two sides and the angle between them, or all three sides and want the angles. Between them they solve any triangle that is actually determined by its inputs.
One honest trap the tool flags for you: the ambiguous case. If you supply two sides and an angle that is not between them (SSA), there can be two different triangles that fit — one acute, one obtuse — because a sine value has two angles under 180°. When that happens the calculator tells you a second solution exists rather than quietly picking one. And three angles with no side describe a shape but not a size: similar triangles all share the same angles, so at least one length is always needed to pin the actual dimensions.
A note on angle units and precision: everything here is in degrees, because that is what drawings and machine controls use, but the results are also given in degrees-minutes-seconds for anyone still setting a vernier protractor or a sine bar. If your job is to set an angle physically to a few arc-seconds, pair this with the sine bar calculator, which converts an angle into the gauge-block stack that produces it — and reminds you that sine-bar resolution falls away badly above 60°.
Trig calculator — FAQ
How do you find a missing side of a right triangle?
If you know the other two sides, use Pythagoras: c = sqrt(a^2 + b^2) for the hypotenuse, or a = sqrt(c^2 - b^2) for a leg. If you know one side and an acute angle, use sohcahtoa: side opposite = hypotenuse x sin(angle), side adjacent = hypotenuse x cos(angle).
What is SOHCAHTOA?
A mnemonic for the three trig ratios in a right triangle: SOH means sine = opposite / hypotenuse, CAH means cosine = adjacent / hypotenuse, TOA means tangent = opposite / adjacent. With any two parts of the triangle known, these three ratios recover the rest.
How do you find an angle from two sides?
Use the inverse trig function of the ratio you have. Angle = arctan(opposite / adjacent), or arcsin(opposite / hypotenuse), or arccos(adjacent / hypotenuse). In a right triangle the two acute angles always add to 90 degrees, so once you have one you have the other.
When do I use the sine rule versus the cosine rule?
Use the sine rule (a/sinA = b/sinB = c/sinC) when you know two angles and any side, or two sides and a non-included angle. Use the cosine rule (c^2 = a^2 + b^2 - 2ab cosC) when you know two sides and the angle between them, or all three sides and want an angle.
What is the ambiguous case (SSA)?
When you know two sides and an angle not between them, the sine rule can give two valid triangles — one with an acute angle and one with its obtuse supplement — because sin(x) = sin(180 - x). This calculator flags when a second solution exists rather than silently choosing one.
Can three angles define a triangle?
No — three angles fix the shape but not the size. Every similar triangle shares the same angles at different scales, so you need at least one side length to determine the actual dimensions.
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