How to use this calculator
- Enter or choose i know.
- The hypotenuse c updates as you type. Use Copy result or Share to keep it.
Method
c² = a² + b²; sin A = a ÷ c, cos A = b ÷ c, tan A = a ÷ b; B = 90° − A; area = ab ÷ 2; altitude = ab ÷ c; inradius = (a + b − c) ÷ 2
- a, b
- legs
- c
- hypotenuse
- A
- angle opposite a
- B
- angle opposite b
Worked example
- c = √(3² + 4²) = 5.
- A = arctan(3 ÷ 4) = 36.8699°, so B = 90° − 36.8699° = 53.1301°.
- Area = 3 × 4 ÷ 2 = 6; perimeter = 3 + 4 + 5 = 12; altitude = 12 ÷ 5 = 2.4.
The 3-4-5 right triangle has angles of about 36.87° and 53.13°, area 6 and perimeter 12.
What the result means
Angles are in degrees. The two acute angles always add up to 90°, so knowing one gives the other.
Assumptions and limits
- One angle is exactly 90°; angle A is opposite leg a.
- Two angles alone fix only the shape, not the size, so at least one side is required.
Questions
What does SOH CAH TOA mean?
Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent. They relate an angle to the sides around it.
How do I find a roof pitch angle?
Treat the rise and the run as the two legs. The pitch angle is arctan(rise ÷ run), which is angle A when a is the rise and b the run.