Calculator Inputs
Choose a method, enter known values, and select preferred units.
Calculation History
No saved calculations yet.
How to Use This Calculator
- Select the calculation method matching your known values.
- Choose length and angle units before entering measurements.
- Enter positive values and confirm the hypotenuse is longest.
- Select precision and rounding preferences for displayed results.
- Press Calculate Triangle to view sides, angles, and checks.
- Copy, print, share, or export the completed calculation.
Formula Reference
θ = tan⁻¹(opposite ÷ adjacent)
θ = sin⁻¹(opposite ÷ hypotenuse)
θ = cos⁻¹(adjacent ÷ hypotenuse)
B = 90° − A
a² + b² = c²
Area = ½ab; P = a + b + c
Worked Examples
| Known values | Method | Key result |
|---|---|---|
| Opposite 3, adjacent 4 | Inverse tangent and Pythagorean theorem | A ≈ 36.8699°, B ≈ 53.1301°, c = 5 |
| Hypotenuse 10, A = 30° | Sine and cosine | Opposite = 5, adjacent ≈ 8.6603 |
| A = 45°, B = 45° | Normalized side ratio | 1 : 1 : √2 |
| 30°–60°–90°, hypotenuse 12 | Preset ratio scaling | Short leg 6, long leg ≈ 10.3923 |
Understanding Right Triangle Angles
A right triangle contains one angle measuring exactly ninety degrees. The remaining two angles are acute and always complementary. Their combined measure must equal ninety degrees.
The opposite side sits across from the selected reference angle. The adjacent side touches that angle without being the hypotenuse. Correct labels determine which trigonometric formula applies.
Sine compares the opposite side with the hypotenuse. Cosine compares the adjacent side with the hypotenuse. Tangent compares the opposite side with the adjacent side.
Inverse trigonometric functions recover angles from known side ratios. Calculators may show answers in degrees, radians, or DMS. Always confirm the selected angle mode before calculating.
The Pythagorean theorem connects all three side lengths. It also confirms whether supplied measurements form a right triangle. The hypotenuse must remain the longest side.
Special triangles provide exact ratios without lengthy decimal calculations. A 45° triangle uses the ratio one, one, root two. A 30° triangle uses one, root three, two.
Area uses half the product of both perpendicular legs. Perimeter equals the sum of every side length. Consistent units prevent incorrect area and perimeter results.
Rounding should happen after all intermediate calculations finish. Early rounding can noticeably change small or extreme triangles. Higher precision improves engineering and surveying comparisons.
This calculator validates inputs before presenting final geometry. It also reports trigonometric ratios and calculation steps. These checks support careful learning and practical measurement work.
Frequently Asked Questions
How many angles does a right triangle have?
A right triangle has three angles. One equals 90°, while the other two total 90°.
Can two acute angles both equal 45°?
Yes. That creates a right isosceles triangle with equal legs.
Why must the hypotenuse be longest?
It lies opposite the 90° angle, which is the triangle's largest angle.
Can I enter radians?
Yes. Select radians as the angle input format before calculating.
What is DMS format?
DMS means degrees, minutes, and seconds. Enter values like 35:20:10.
What happens when only two angles are known?
The calculator verifies them and returns normalized side ratios.
How is the missing acute angle found?
Subtract the known acute angle from 90°.
Why can rounding change the result?
Rounded intermediate values can accumulate error. Keep full precision until the end.
Can results be saved?
Yes. Use copy, CSV, PDF, print, share, or browser history tools.