Right Triangle Calculator
Enter any two sides to calculate the third using the Pythagorean Theorem.
Understanding the Right Triangle
A right triangle is a specific type of triangle where one of the interior angles measures exactly 90 degrees (a right angle). This geometric shape is the foundation of trigonometry and plays a crucial role in physics, engineering, construction, and mathematics.
The Pythagorean Theorem
The relationship between the sides of a right triangle is defined by the Pythagorean Theorem. It states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
a² + b² = c²
- Leg A and Leg B: The two sides that form the 90-degree angle.
- Hypotenuse (Side C): The longest side, located opposite the right angle.
How to Use the Calculator
This tool allows you to solve for any missing side of a right triangle. Simply input any two known values, and the calculator will determine the third side, the total area, the perimeter, and the two remaining interior angles.
Practical Example
Imagine you are leaning a 10-foot ladder against a wall. If the base of the ladder is 6 feet away from the wall, how high does the ladder reach?
- Side C (Hypotenuse) = 10 (the ladder length).
- Side B (Leg) = 6 (distance from the wall).
- Using the formula: 10² = a² + 6² → 100 = a² + 36 → a² = 64 → a = 8 feet.
Key Properties of Right Triangles
- The sum of the two non-right angles is always exactly 90 degrees (they are complementary).
- The area is calculated as 1/2 × base × height, which is 0.5 × a × b.
- The hypotenuse is always the longest side of the triangle.
- Special right triangles like the 3-4-5 or 5-12-13 triangles are common in geometry problems because their side lengths are whole numbers (Pythagorean triples).