A right triangle contains one 90-degree angle. With enough known measurements, you can calculate its missing sides and acute angles. A right triangle calculator can help check your geometry calculations.
Right triangle parts explained
The hypotenuse is opposite the right angle and is the longest side. The other two sides are called legs. Relative to a chosen acute angle, one leg is opposite and the other is adjacent.
How to use a right triangle calculator
- Open the Right Triangle Calculator.
- Identify which side lengths or angles you already know.
- Enter the known measurements in the corresponding fields supported by the tool.
- Calculate the missing values.
- Verify that the acute angles sum to 90 degrees and the side lengths satisfy the Pythagorean theorem.
Pythagorean theorem for missing sides
For legs a and b and hypotenuse c, a² + b² = c². If a = 6 cm and b = 8 cm, then c = √(36 + 64) = 10 cm. If c and one leg are known, rearrange the equation: a = √(c² − b²).
Finding angles using trigonometry
For an acute angle θ, sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, and tan θ = opposite / adjacent. To recover an angle from a side ratio, use the appropriate inverse function: arcsin, arccos, or arctan.
Worked example: a 3–4–5 triangle
Suppose the side opposite θ is 3 and the adjacent side is 4. The hypotenuse is 5. Then tan θ = 3/4, so θ ≈ 36.87°. The other acute angle is approximately 53.13°. Together they add to 90°.
Area and perimeter
The area of a right triangle is (a × b) / 2, where a and b are the perpendicular legs. Its perimeter is a + b + c. For a 6–8–10 triangle, area = 6 × 8 ÷ 2 = 24 square units and perimeter = 24 units.
Useful right triangle formulas
| Quantity | Formula |
|---|---|
| Hypotenuse | c = √(a² + b²) |
| Missing leg | a = √(c² − b²) |
| Area | A = ab / 2 |
| Perimeter | P = a + b + c |
| Acute angles | θ + φ = 90° |
Common mistakes
- Applying right-triangle formulas to a triangle without a 90-degree angle.
- Confusing opposite and adjacent sides when changing the reference angle.
- Using radians when the expected answer is in degrees.
- Entering side lengths with inconsistent units.
- Assuming a single side length determines a unique right triangle.
Frequently asked questions
Can a right triangle have two 90-degree angles?
No. Its interior angles total 180 degrees, so only one angle can be 90 degrees.
Are the two acute angles always complementary?
Yes. They sum to 90 degrees.
Can I calculate a triangle from only one side?
No. You need additional independent information, such as another side or an acute angle.
How do I find the area without the hypotenuse?
Multiply the two perpendicular leg lengths and divide by two.
Check your results with the Right Triangle Calculator.
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