Equation-first triangle helper
Right Triangle Solver
Enter any 2 known values, sides or angles, and this solver finds all remaining sides, angles, area, and perimeter. Full step-by-step working included.
- Sides
- Angles
- Area
- Perimeter
- Step-by-step
Core solver
Right Triangle Solver
Result
Enter values to calculate the missing side or verify a triangle.
Show calculation steps
Recent calculations
Need angle-driven cases like one side plus one acute angle? Use the all-cases solver below or open the Right Triangle Calculator for the broader workflow.
All-Cases Right Triangle Solver
Supports SSS, SAS, ASA, AAS, and HL so you can solve from side-angle combinations too.
Method
How to Solve a Right Triangle
Solving a right triangle means finding all unknown sides and angles given some known values. A
right triangle has three sides, a, b, c, and three angles,
A, B, and the fixed 90° right angle. You need at least two
known values, and at least one of them must be a side, to fully solve the triangle.
Known: both legs a and b
Method: Use c = √(a² + b²) for the hypotenuse, then tan⁻¹(a/b) for one acute angle.
Tool: Pythagorean theorem first, then inverse tangent for the angles.
Known: one leg and hypotenuse
Method: Use a = √(c² − b²) or b = √(c² − a²), then sin⁻¹(a/c) for the acute angles.
Tool: Rearranged Pythagorean theorem plus inverse sine.
Known: one side and one acute angle
Method: Use trigonometric ratios, sin, cos, or tan, to find the remaining sides.
Tool: Use the all-cases solver above for SAS, ASA, AAS, and HL-style setups.
This page keeps the familiar 3-tab solver for direct side workflows, then adds the all-cases right triangle solver for angle input and full triangle solving.
Decision tree
Which Solver Tab Should I Use?
(a and b)
Find Hypotenuse
one leg
Find Missing Leg
If you have all three sides and want to verify that the triangle is right-angled, use the Verify Triangle tab. If your known values include an angle, use the all-cases solver in Section 2.
FAQ
Frequently Asked Questions
Solving a right triangle means finding the values of all unknown sides and angles. A right
triangle has six measurements: three sides, a, b, c,
and three angles, A, B, and 90°. Given any two values,
with at least one being a side, you can calculate the remaining values using the Pythagorean
theorem and trigonometry.
You need exactly two known values, and at least one must be a side length. Knowing only two angles is not enough because angles alone determine shape, not size.
Yes. Once the side lengths are known, the solver can calculate the acute angles with inverse
trigonometric functions such as arctan and arcsin. The all-cases
solver on this page also accepts side-angle combinations directly.
In practice, they overlap. A calculator emphasizes computation, while a solver emphasizes finding every missing value from the information you already know. This page does both: it computes the result and shows the step-by-step reasoning.
No. This page is designed for right triangles. For oblique triangles, you would need tools based on the Law of Sines or Law of Cosines instead of the right-triangle relationships used here.
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