Right Triangle Calculator

Hypotenuse, angle, and ratios from two legs with SOHCAHTOA.

What it does

Right triangles resolve through two facts: Pythagoras builds the hypotenuse from the legs while SOHCAHTOA reads every ratio off the sides. Legs 3 by 4 give hypotenuse 5 at 36.87 degrees with sine 0.6.

The tool above takes opposite with adjacent legs. It returns hypotenuse, acute angle, and sine beside them. Cosine, tangent, and reciprocals ride in the note.

Ratios match OpenStax precalculus in both editions: sine as opposite over hypotenuse, cosine adjacent over, tangent opposite over adjacent, with the 3-4-5 triangle reading 0.8, 0.6, and 1.333 across its angles. Special triangles extend the pattern with exact roots for 30, 45, and 60 degrees.

Angle always faces its opposite leg, and the hypotenuse always faces the right angle as the longest side. Either acute angle works with flipped opposite and adjacent labels.

How to use

1. Type the opposite leg to your angle.
2. Type the adjacent leg.
3. Read hypotenuse first, angle beside it.
4. Read sine, then ratios in the note.
5. Flip labels for the other acute angle.
6. Keep units matched across legs.

Formula

o, a

Opposite and adjacent legs to the angle.

h

Hypotenuse from Pythagoras.

SOHCAHTOA

Sine/cosine/tangent ratio memory.

Reciprocals follow: secant is h/a, cosecant h/o, cotangent a/o. Degrees out; multiply by pi/180 for radians.

Worked example

Reference table

Limits

• Right triangles only.
• Legs input; hypotenuse solves.
• Degrees out by default.
• Flat geometry; spheres differ.

Common mistakes

• Labeling hypotenuse as a leg.
• Reading sine off the wrong angle.
• Mixing degrees with radians.
• Forgetting which leg is opposite.
• Trusting rounded angles in chains.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• OpenStax Precalculus 2e: Right Triangle Trigonometry
• OpenStax Precalculus: Right Triangle Trigonometry

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