Right Triangle Calculator — Quick & Accurate Online Calculator & Guide
Solve right triangles using the Pythagorean theorem and SOH CAH TOA trigonometry. Find sides, angles, area, and perimeter with a dynamic SVG triangle and.
Right Triangle
Results below
Enter Values
Triangle Area
6
Perimeter
12
Angle A (opposite leg a)
36.8699°
Angle B (opposite leg b)
53.1301°
SOH Step
sin(α) = opposite/hypotenuse = a/c = 3/5 = 0.6000 → α = 36.87°
CAH Step
cos(α) = adjacent/hypotenuse = b/c = 4/5 = 0.8000 → α = 36.87°
TOA Step
tan(α) = opposite/adjacent = a/b = 3/4 = 0.7500 → α = 36.87°
Scenario Comparison
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Step-by-Step Proof
Isolate the variable: c = √(a² + b²)
SOH CAH TOA — Finding Angles
SOH sin(α) = Opposite / Hypotenuse = a / c = 3 / 5 = 0.6000
CAH cos(α) = Adjacent / Hypotenuse = b / c = 4 / 5 = 0.8000
TOA tan(α) = Opposite / Adjacent = a / b = 3 / 4 = 0.7500
α = sin⁻¹(0.6000) = 36.8699° | β = 90° − α = 53.1301°
Leg a
3
Leg b
4
Hypotenuse c
5
Pythagorean Theorem
a² + b² = c²
Hypotenuse
c = √(a² + b²)
Leg a
a = √(c² − b²)
Leg b
b = √(c² − a²)
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