Right Triangle Calculator · Practical guide
Right Triangle Calculator with One Side and One Angle
One side plus one acute angle is all it takes — trigonometry fills in every other side, angle, the area, and the perimeter.
At a glance
Yes — Two Values Are Enough
Knowing one side and one acute angle completely determines a right triangle. Since the right angle is already 90°, the second acute angle is just 90° minus the one you know, and sine, cosine, and tangent recover the remaining sides. For example, side A = 6 with angle A = 30° gives a hypotenuse of 12 and side B of about 10.3923.
Interactive tool
Right Triangle Calculator
Enter your own values, then compare the result with the examples below.
Right Triangle Solution
The Three Formulas
Which formula applies depends on where your known side sits relative to the known angle:
- Known side is opposite the angle: hypotenuse = a ÷ sin(A), other leg = a ÷ tan(A)
- Known side is adjacent to the angle: hypotenuse = b ÷ cos(A), other leg = b × tan(A)
- Known side is the hypotenuse: a = c × sin(A), b = c × cos(A)
Worked Example: Side 6, Angle 30°
| Property | Value | Formula Used |
|---|---|---|
| Angle B | 60° | 90° − 30° |
| Hypotenuse | 12 | 6 ÷ sin(30°) |
| Side B | 10.3923 | 6 ÷ tan(30°) |
| Area | 31.1769 | (6 × 10.3923) ÷ 2 |
| Perimeter | 28.3923 | 6 + 10.3923 + 12 |
What Two Values Cannot Do
Two angles alone cannot solve a triangle — they fix the shape but not the size, since infinitely many similar triangles share the same angles. You always need at least one side length. Also note the calculator works in degrees, not radians, and the known angle must be between 0° and 90°. Enter your side and angle above to get the complete solution instantly.
Frequently Asked Questions
Can I solve a right triangle with the hypotenuse and one angle?
Yes. The legs are c × sin(A) and c × cos(A). For a hypotenuse of 10 and an angle of 30°, the legs are 5 and about 8.6603.
What if I know two sides instead?
That also fully solves the triangle: the Pythagorean theorem gives the third side, and arctangent gives the angles. Two sides or one side plus one angle both work.
Should the angle be entered in degrees or radians?
Degrees. Enter 30 for a 30° angle. All results are displayed in degrees as well.
Why does my angle have to be less than 90°?
A right triangle already has one 90° angle, and the three angles must sum to 180°, so each acute angle must fall strictly between 0° and 90°.