Find the hypotenuse, area, perimeter and angles of a right triangle.
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How do you calculate a right triangle's hypotenuse and area?
Hypotenuse c = √(a² + b²); area = ½ × a × b; and the angles come from the arctangent of the opposite over adjacent sides. This assumes a right angle between the two legs a and b. For example, legs of 3 and 4 give a hypotenuse of 5 and an area of 6.
Understanding your result
This assumes a right angle between sides a and b.
Formula and method
Hypotenuse c = √(a² + b²); area = ½ × a × b; angles come from the arctangent of the opposite over adjacent sides.
Assumptions and limitations
It applies only to right-angled triangles, taking the two legs that meet at the 90-degree corner as its input. It will not solve scalene or obtuse triangles, and it assumes your two given sides are the legs rather than a leg and the hypotenuse.
Worked example
Legs of 3 and 4 give a hypotenuse of 5 and an area of 6.
How to use this tool
- Enter side a and side b (the legs).
- Press Calculate.
Common mistakes to avoid
- Entering the hypotenuse as one of the legs.
About the Right Triangle Calculator
Enter the two legs of a right triangle to find the hypotenuse, area, perimeter and the two acute angles.
Who should use this tool
Geometry students verifying answers, carpenters and builders squaring corners and cutting rafters, and DIY hobbyists who know two sides meeting at a right angle and need the hypotenuse, area, perimeter and the two acute angles worked out.
Benefits
- Applies the Pythagorean theorem to find the hypotenuse
- Returns area, perimeter and both acute angles together
- Derives angles from the arctangent of the sides
- Confirms a corner is truly square for building work
Practical use cases
- Checking the diagonal brace length for a squared frame
- Verifying a geometry answer for the hypotenuse
- Cutting a rafter to the right length and angle
- Finding the area of a triangular section from its legs
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
How are the two acute angles calculated?
Each acute angle comes from the arctangent of the opposite leg divided by the adjacent leg. The two acute angles always add up to 90 degrees, because the third angle is the right angle. For legs of 3 and 4, they work out to roughly 36.87 and 53.13 degrees.
Can I enter the hypotenuse instead of the two legs?
This tool expects the two legs that meet at the right angle. If you know the hypotenuse and one leg, subtract the square of that leg from the square of the hypotenuse, then take the square root to recover the missing leg first.