Give this tool any two known values — sides and/or an acute angle — and it solves the rest of a right triangle: the missing sides via the Pythagorean theorem, both acute angles via SOHCAHTOA, plus the area and perimeter. Useful for geometry, trigonometry homework, construction layout, and surveying.
How it works
The right angle sits at vertex C, with angle A opposite leg a, angle B opposite leg b, and the hypotenuse c opposite the right angle. Depending on the two values you supply, the solver applies:
- Two legs: c = √(a² + b²); angle A = arctan(a ÷ b).
- Leg and hypotenuse: the other leg = √(c² − leg²); angles from arcsin/arccos.
- Side and acute angle: the missing sides come from sin, cos, or tan of the angle (SOHCAHTOA).
It always uses that the two acute angles sum to 90°, then computes area = ½ × a × b and perimeter = a + b + c.
Example
Legs a = 3 and b = 4:
- Hypotenuse c = √(3² + 4²) = √25 = 5
- Angle A = arctan(3 ÷ 4) ≈ 36.87°
- Angle B = 90 − 36.87 = 53.13°
- Area = ½ × 3 × 4 = 6
- Perimeter = 3 + 4 + 5 = 12
| Known | Find sides with | Find angles with |
|---|---|---|
| Two legs | Pythagoras | arctan |
| Leg + hypotenuse | Pythagoras | arcsin / arccos |
| Side + angle | sin / cos / tan | 90° − known angle |
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