Formula Used
A right triangle has one fixed angle of 90 degrees.
A + B = 90°
c² = a² + b²
sin(A) = a / c
cos(A) = b / c
tan(A) = a / b
Area = ab / 2
Perimeter = a + b + c
How to Use This Calculator
Enter any two sides to solve the triangle.
You may also enter one acute angle and one side.
Leave unknown fields empty.
Select degrees or radians for angle input.
Press Calculate to view results above the form.
Use CSV or PDF buttons to export the same result.
Example Data Table
| Side a | Side b | Hypotenuse | Angle A | Angle B |
|---|---|---|---|---|
| 3 | 4 | 5 | 36.8699° | 53.1301° |
| 5 | 12 | 13 | 22.6199° | 67.3801° |
| 8 | 15 | 17 | 28.0725° | 61.9275° |
Right Triangle Angle Measures Guide
Purpose
This calculator helps find missing angle measures in a right triangle. It also finds sides when enough information is supplied. A right triangle always contains one right angle. The other two angles are acute. They must add to ninety degrees.
Input Method
You can enter two sides. The tool then applies the Pythagorean theorem. It finds the missing side first. Next, it uses inverse trigonometric ratios. These ratios return the two acute angles. You can also enter one angle and one side. This method is useful when a drawing gives a slope angle, elevation angle, or depression angle.
Side Labels
Side a is opposite angle A. Side b is opposite angle B. Side c is the hypotenuse. The hypotenuse is always opposite the right angle. It is the longest side. Correct labels are important. Wrong labels can swap the acute angles.
Advanced Results
The calculator also returns area, perimeter, height to the hypotenuse, inradius, circumradius, and trigonometric ratios. These values help in geometry, surveying, construction, navigation, and classroom work. They also help check whether a triangle is realistic. If the hypotenuse is smaller than a leg, the triangle is invalid.
Accuracy
Decimal precision can be changed. More decimal places give a more detailed answer. Fewer places give cleaner output. Small rounding differences are normal. They happen because trigonometric functions use decimal approximations.
Best Practice
Start with the clearest known values. Use measured side lengths when possible. Use angle input only when the angle is trusted. If both acute angles are entered, their sum must be ninety degrees. If one angle is entered, the other is calculated automatically.
Exports
The CSV option is useful for spreadsheets. The PDF option is useful for printing or saving. Both exports include the same calculated measures shown on the page.
FAQs
Can this calculator find both acute angles?
Yes. Enter two valid sides, or enter one acute angle. The other acute angle is found because both acute angles add to 90 degrees.
What is the hypotenuse?
The hypotenuse is the longest side of a right triangle. It is always opposite the 90 degree angle.
Can I use radians?
Yes. Select radians before calculating. The calculator converts the entered angle internally and solves the triangle.
Why do I need two known values?
A triangle needs enough information to be solved. Two sides, or one side with one acute angle, define a right triangle scale.
What happens if I enter all sides?
The calculator uses the supplied side values and checks the right triangle relationship through the computed measures.
Can this solve non-right triangles?
No. This calculator is designed for right triangles only. One angle is always treated as 90 degrees.
Why are my answers rounded?
Results are rounded by the selected decimal precision. Increase precision to see more decimal places.
What do side a and side b mean?
Side a is opposite angle A. Side b is opposite angle B. Correct labeling helps produce the expected angle placement.