Right Triangle Calculator
Solve all sides, acute angles, perimeter, area, and trigonometric ratios for any right-angled triangle.
Hypotenuse c
5
Area
6
Perimeter
12
Angle A (opposite a)
36.869898°
Angle B (opposite b)
53.130102°
Angle C
90°
sin A
0.6
cos A
0.8
tan A
0.75
How to Use the Right Triangle Calculator
- Enter the lengths of leg a and leg b.
- The calculator computes the hypotenuse c, angles A and B in degrees, area, and perimeter.
- Inspect the exact trigonometric ratios: sin(A), cos(A), and tan(A).
Formulas & Principles
Hypotenuse: c = √(a² + b²)
Angle A: A = arctan(a / b) × (180 / π)
Angle B: B = arctan(b / a) × (180 / π)
Area: A = 0.5 × a × b | Perimeter: P = a + b + c
Trig: sin(A) = a/c, cos(A) = b/c, tan(A) = a/b
Frequently Asked Questions
What is the sum of angles in a right triangle?
The sum of all three internal angles is always 180°. With the right angle at 90°, the two acute angles always sum to 90° (A + B = 90°).
How are trigonometry functions related to right triangles?
SOH-CAH-TOA: sin(A) = opposite/hypotenuse (a/c), cos(A) = adjacent/hypotenuse (b/c), tan(A) = opposite/adjacent (a/b).
How is right triangle area calculated?
Because the legs are perpendicular, the area is simply half the product of the legs: Area = 0.5 × a × b.
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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