Right Triangle Calculator

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Input Values

Please provide 2 values below to calculate the other values of a right triangle.

Side a (Adjacent)

Side b (Opposite)

Side c (Hypotenuse)

Angle α (degrees)

Angle β (degrees)

Triangle Visualization

Properties

Formulas

Special Triangles

Right Triangle

Side a (Adjacent): 3

Side b (Opposite): 4

Side c (Hypotenuse): 5

Angle α: 36.87° = 36°52′12″ = 0.6435 rad

Angle β: 53.13° = 53°7′48″ = 0.9273 rad

Area: 6

Perimeter: 12

Altitude (h): 2.4

Pythagorean Theorem: a² + b² = c²

Area Formula: A = (1/2) × a × b

Perimeter Formula: P = a + b + c

Altitude Formula: h = (a × b) / c

Angle Formulas: sin(α) = Opposite/Hypotenuse

cos(α) = Adjacent/Hypotenuse

tan(α) = Opposite/Adjacent

30°-60°-90° Triangle: Ratio: 1 : √3 : 2

45°-45°-90° Triangle: Ratio: 1 : 1 : √2

Pythagorean Triples: 3-4-5, 5-12-13, 7-24-25, etc.

Calculation Steps

Given: Side a = 3, Side c = 5

Using Pythagorean theorem: b = √(c² - a²) = √(25 - 9) = √16 = 4

Angle α = arctan(opposite/adjacent) = arctan(4/3) ≈ 53.13°

Angle β = 90° - α ≈ 90° - 53.13° = 36.87°

Area = (1/2) × a × b = (1/2) × 3 × 4 = 6

Perimeter = a + b + c = 3 + 4 + 5 = 12

Altitude h = (a × b) / c = (3 × 4) / 5 = 12/5 = 2.4

About Right Triangles

Right Triangle Properties

A right triangle is a type of triangle that has one angle that measures 90°. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry.

In a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.

Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

If the lengths of both legs (a and b) are known, then the hypotenuse can be calculated as: c = √(a² + b²)