Geometry
Right Triangle Solver
Enter both perpendicular legs and the solver returns the hypotenuse, perimeter, area, altitude to the hypotenuse, and the acute angles.
Plug in both legs to get the hypotenuse, area, perimeter, altitude to the hypotenuse, and acute angles.
Pythagorean & trig relationships
c = √(a² + b²) Area = (ab)/2 Altitude to c = (ab)/c
Angles are derived from tan(A) = a/b and tan(B) = b/a, keeping the right angle locked at 90°. The altitude splits the hypotenuse into segments useful for drafting elevations.
How to use
- Measure both legs (sides that form the right angle) in the same unit.
- Enter those values and optionally adjust decimal precision.
- Read the full triangle solution—hypotenuse, area, perimeter, altitude, and acute angles.
Example
Input: Leg a = 3 ft, Leg b = 4 ft
Output: Hypotenuse = 5 ft, Area = 6 ft², Altitude to hypotenuse ≈ 2.4 ft
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Right Triangle Solver: Right Triangle Solver. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Right Triangle Solver: Computes hypotenuse, area, perimeter, and angles from the two legs. It's built around right triangle, pythagorean, hypotenuse, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Angles are derived from tan(A) = a/b and tan(B) = b/a, keeping the right angle locked at 90°. The altitude splits the hypotenuse into segments useful for drafting elevations. The core relationship is c = √(a² + b²) Area = (ab)/2 Altitude to c = (ab)/c, shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Measure both legs (sides that form the right angle) in the same unit. (2) Enter those values and optionally adjust decimal precision. (3) Read the full triangle solution—hypotenuse, area, perimeter, altitude, and acute angles. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering Leg a = 3 ft, Leg b = 4 ft returns Hypotenuse = 5 ft, Area = 6 ft², Altitude to hypotenuse ≈ 2.4 ft. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Can I enter decimals?
Yes. The calculator works with whole numbers or decimals so you can enter metric or imperial dimensions.
What if I only know the hypotenuse?
Provide both legs for a full solution. If you know a hypotenuse and one leg, solve for the other leg with a² + b² = c² before pasting those values here.
What formula does the Right Triangle Solver use?
Angles are derived from tan(A) = a/b and tan(B) = b/a, keeping the right angle locked at 90°. The altitude splits the hypotenuse into segments useful for drafting elevations.
How do I use the Right Triangle Solver?
Measure both legs (sides that form the right angle) in the same unit. Enter those values and optionally adjust decimal precision. Read the full triangle solution—hypotenuse, area, perimeter, altitude, and acute angles.