Right Triangle Solver

Given any 2 of (a, b, c, angle), solve all remaining sides + angles.

Inputs

Result

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General calculation reads

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How Not to Be Wrong
Jordan Ellenberg - math thinking
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The Joy of X
Steven Strogatz - accessible math
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Pick what's given.
  • Enter the two known values.
  • Read all sides and angles.

About this calculator

A right triangle has one 90° angle (C). Given any 2 pieces of (a, b, c, angle A), the remaining 2 are determined. Common cases: SOHCAHTOA — sin(A) = opposite/hypotenuse = a/c; cos(A) = b/c; tan(A) = a/b. Pythagoras: a² + b² = c². The simplest right triangle math case that students see; foundation for surveying and 3D vector decomposition.

Frequently asked

What's SOHCAHTOA?+
Mnemonic for trig ratios in right triangles. SOH: Sin = Opp/Hyp. CAH: Cos = Adj/Hyp. TOA: Tan = Opp/Adj.
How do you find angles?+
arcsin, arccos, arctan — inverse trig. JS: Math.asin, Math.acos, Math.atan, Math.atan2.
What's atan2 vs. atan?+
atan(y/x) loses sign info. atan2(y,x) preserves quadrant. Calc uses atan2 for robust angle extraction.
Why area = ½ab?+
Right triangle = half a rectangle of sides a,b. Area = ½ × base × height; here base and height are the legs.
30-60-90 ratios?+
Special: short leg = c/2, long leg = c√3/2, hypotenuse = c. Showcases exact arctangent/arcsine values.

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P = a + b + c. Sum of all three sides.

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