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Free right triangle calculator to find all sides, angles, area, and perimeter. Calculate from two sides or one side and angle with detailed solutions.
Calculate all properties of a right triangle from two known values
A right triangle (also called a right-angled triangle) is a triangle with one angle measuring exactly 90 degrees. This fundamental geometric shape is essential in mathematics, engineering, construction, and countless real-world applications. The Pythagorean theorem, one of the most important mathematical principles, applies exclusively to right triangles.
Choose Calculation Method: Select "Two Sides" if you know any two sides (legs or hypotenuse), or "Side & Angle" if you know one side and one non-right angle.
Select Measurement Unit: Choose from millimeters (mm), centimeters (cm), meters (m), inches (in), or feet (ft) based on your needs.
Enter Known Values: Input your measurements accurately. Specify whether each side is a leg (a or b) or the hypotenuse (c). For angles, specify A or B (not the 90° angle).
Calculate Results: Click the calculate button to instantly compute all triangle properties using proven mathematical formulas.
Review Complete Solution: View all calculated values including sides, angles, area, perimeter, and detailed step-by-step mathematical solutions showing how each value was derived.
Formula: a² + b² = c²
Find any side when you know the other two sides
Formula: Area = (a × b) / 2
Area equals half the product of the two legs
Formula: P = a + b + c
Sum of all three sides
sin(A) = a/c, cos(A) = b/c, tan(A) = a/b
SOH-CAH-TOA for finding angles and sides
Angles: 45°, 45°, 90°
Side Ratio: 1 : 1 : √2
Properties: Two legs are equal (a = b)
Example: If legs = 5, then hypotenuse = 5√2 ≈ 7.071
Angles: 30°, 60°, 90°
Side Ratio: 1 : √3 : 2
Properties: Hypotenuse is twice the shortest side
Example: If short leg = 4, then long leg = 4√3 ≈ 6.928, hypotenuse = 8
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A right triangle is a triangle with one 90-degree angle. It has three sides: two legs (a and b) that form the right angle, and the hypotenuse (c) which is the longest side opposite the right angle.
Use the Pythagorean Theorem (a² + b² = c²) when you know two sides. Use trigonometric functions (sin, cos, tan) when you know one side and one non-right angle. This calculator automatically applies the correct method based on your inputs.
Area = (a × b) / 2, where a and b are the two legs. For example, if a=6 and b=8, then Area = (6 × 8) / 2 = 24 square units.
Use inverse trigonometric functions: Angle A = arctan(a/b) or arcsin(a/c) or arccos(b/c). One angle is always 90°, and the other two angles sum to 90°.
Special right triangles: 45-45-90 triangle (sides ratio 1:1:√2) and 30-60-90 triangle (sides ratio 1:√3:2). These have predictable side ratios useful for quick calculations.
Problem: A right triangle has legs a = 3 cm and b = 4 cm. Find all other properties.
Solution:
Problem: A right triangle has hypotenuse c = 13 m and leg a = 5 m. Find all properties.
Solution:
Problem: A right triangle has hypotenuse c = 10 ft and angle A = 30°. Find all properties.
Solution:
Problem: An isosceles right triangle has legs of 7 inches. Find all properties.
Solution:
Find missing side of right triangle
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Calculate from two sides or one side and angle
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