Right Triangle Calculator

A right triangle has one 90° angle. Given any two side lengths (or one side and one angle), this calculator solves for everything: all three sides, both acute angles, area, and perimeter.

How to Use This Calculator

1. Enter any two known values: sides (a, b, c) or one side and one acute angle.
2. Click Calculate to find all missing sides, angles, area, perimeter, and trig ratios.

Key Formulas

Sides: a² + b² = c² (Pythagorean theorem)

Trigonometric ratios (for angle A):
sin(A) = opposite/hypotenuse = a/c
cos(A) = adjacent/hypotenuse = b/c
tan(A) = opposite/adjacent = a/b

Angles: A + B = 90° (complement); A + B + 90° = 180°

Area: ½ × a × b

Example: Given One Side and One Angle

Hypotenuse c = 13, angle A = 35°

• a = c × sin(A) = 13 × sin(35°) ≈ 7.46
• b = c × cos(A) = 13 × cos(35°) ≈ 10.65
• Angle B = 90° − 35° = 55°
• Area = ½ × 7.46 × 10.65 ≈ 39.7

SOHCAHTOA Memory Aid

Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent

Common Mistakes to Avoid

• Mislabeling opposite and adjacent — These depend on which angle you're working from. The opposite side is across from the angle; adjacent is next to it (but not the hypotenuse).
• Using degrees when calculator is in radian mode — Always check your trig calculator mode. sin(30°) ≠ sin(30 radians).
• Assuming the hypotenuse is always side c — The hypotenuse is the side opposite the right angle, whichever side that is in your labeling.

Frequently Asked Questions

What are the special right triangles?

45-45-90: sides are x, x, x√2. If legs = 5, hypotenuse = 5√2 ≈ 7.07.
30-60-90: sides are x, x√3, 2x. If short leg = 4, long leg = 4√3 ≈ 6.93, hypotenuse = 8.

How is this used in real life?

Building ramps, roofs, and staircases; navigation (bearing + distance → coordinates); engineering (force components); surveying (indirect measurement of heights and distances).

Can I solve a right triangle with just two angles?

No — you need at least one side length. Knowing all angles determines the shape but not the size of the triangle. Any similar triangle has the same angles but different side lengths.

Conclusion

Right triangles are everywhere in mathematics, engineering, and everyday life. This calculator solves any right triangle from any two known values — giving you all sides, angles, and measurements in one step.

Related: Pythagorean Theorem Calculator | Triangle Calculator | Slope Calculator | Scientific Calculator