Advanced Right Triangle Solver Calculator

Right Triangle Solver Form

Notation used: leg a is opposite angle A, leg b is adjacent to angle A, and c is the hypotenuse.

Choose any supported pair of known values. The solver computes all remaining sides, acute angles, area, perimeter, radii, altitude, median, and a geometry check.

Solve mode

Decimal precision

Unit label

Leg a

Leg b

Hypotenuse c

Angle A (degrees)

Example Data Table

These examples show common solve paths and expected outputs for quick checking.

Case	Known Inputs	Solved Outputs	Use Case
1	a = 3, b = 4	c = 5, A = 36.87°, B = 53.13°, Area = 6	Classic geometry check
2	A = 30°, c = 10	a = 5, b = 8.6603, Area = 21.6506	Survey and layout work
3	A = 45°, b = 12	a = 12, c = 16.9706, Area = 72	Balanced right triangle
4	c = 13, a = 5	b = 12, A = 22.62°, B = 67.38°, Perimeter = 30	Field verification

Formulas Used

Core side and angle relations

c² = a² + b²
A = arctan(a / b)
B = 90° - A
a = c × sin(A)
b = c × cos(A)
a = b × tan(A)
b = a / tan(A)

Derived geometry metrics

Area = (a × b) / 2
Perimeter = a + b + c
Altitude to hypotenuse = (a × b) / c
Median to hypotenuse = c / 2
Inradius = (a + b - c) / 2
Circumradius = c / 2
Residual = c² - a² - b²

How to Use This Calculator

Select the input pair that matches the values you already know.
Enter the known side lengths or angle, then choose the precision and your preferred unit label.
Submit the form to solve the triangle and review the full result set above the form.
Inspect the plotted triangle, derived metrics, and residual check for confidence.
Download the results as CSV for spreadsheets or PDF for reports and documentation.

FAQs

1) What information is enough to solve a right triangle?

You need any two independent values, and at least one must be a side. Examples include two legs, one leg and the hypotenuse, or one acute angle with one side.

2) Why must the angle stay between 0° and 90°?

A right triangle already contains one 90° angle. The remaining two angles must therefore be acute, so each one must be greater than 0° and less than 90°.

3) What does the Pythagorean residual show?

It measures how close the solved values are to the identity c² = a² + b². A value near zero means the triangle is numerically consistent.

4) What is the difference between leg a and leg b?

In this layout, leg a is opposite angle A, while leg b is adjacent to angle A. The naming keeps the trigonometric formulas consistent throughout the page.

5) Can I use any unit system?

Yes. Enter lengths in any consistent unit, such as millimeters, meters, feet, or inches. The calculator keeps the same unit label throughout the results.

6) Why do area units appear squared?

Area is measured in square units because it represents surface coverage. If your side unit is meters, the area output is shown in square meters.

7) When is this solver useful outside classwork?

It helps with layout design, roof checks, accessibility ramps, framing, surveying, navigation, and any task where a right-angle triangle describes the geometry.

8) What do the CSV and PDF downloads include?

They export the solved metrics shown in the result table. The PDF also adds a clean title, summary information, and the plotted triangle image when available.