Complete guide
Right triangle calculator for sides, angles and area
Choose the known side, enter its length and one acute angle. Calculator24 solves both legs, the hypotenuse, complementary angle, area and perimeter.
Solve a right triangle
A right triangle already has a 90° angle. One additional acute angle and one side determine the remaining sides and angle.
Sine, cosine and tangent
Relative to angle A, a is opposite, b is adjacent and c is the hypotenuse.
sin A=a/ccos A=b/ctan A=a/bComplementary angle
The two acute angles sum to 90°, so B=90°−A. Angles near either boundary can make one leg extremely small or large relative to the other.
Special right triangles
A 45-45-90 triangle has side ratio 1:1:√2. A 30-60-90 triangle has short-leg, long-leg and hypotenuse ratio 1:√3:2.
Area and perimeter
The perpendicular legs form base and height, so area is ab/2. Perimeter is a+b+c.
Special triangle ratios
| Angles | Ratio |
|---|---|
| 45°-45°-90° | 1 : 1 : √2 |
| 30°-60°-90° | 1 : √3 : 2 |
Frequently asked questions
What information solves a right triangle?
One acute angle and one side are sufficient because the right angle is known.
Which side is the hypotenuse?
It is opposite the 90° angle and is the longest side.
Do acute angles add to 90 degrees?
Yes, because all triangle angles total 180°.
How is triangle area calculated?
Multiply the two perpendicular legs and divide by two.
Can I enter 0 or 90 degrees?
No. Those boundary values do not form a nondegenerate right triangle.
What to keep in mind
This solves Euclidean right triangles. The entered angle must be greater than 0° and less than 90°.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.