A right angle triangle, also known as a right triangle, is a fundamental shape in geometry. It is defined as a triangle in which one of the angles is a right angle (exactly 90 degrees). The sides adjacent to the right angle are called "legs" (or "cathetus"), and the side opposite the right angle is called the "hypotenuse".
Key Properties and Formulas:
Pythagorean Theorem: This is the most famous property of right triangles. It states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is:
a² + b² = c²
This theorem allows us to find the length of any side if the lengths of the other two sides are known.
Area: The area of a right triangle is half the product of its two legs.
Area = ½ × base × height
In a right triangle, the legs serve as the base and height.
Perimeter: The perimeter is the sum of the lengths of all three sides.
Perimeter = a + b + c
Trigonometric Ratios: The sine (sin), cosine (cos), and tangent (tan) of the angles (other than the right angle) are also important. For an angle θ:
sin(θ) = Opposite / Hypotenuse
cos(θ) = Adjacent / Hypotenuse
tan(θ) = Opposite / Adjacent
Use Cases:
Right angle triangles are ubiquitous in various fields:
Construction and Architecture: Ensuring corners are square, calculating roof slopes, and structural stability.
Navigation: Determining distances and positions using triangulation.
Engineering: Designing structures, calculating forces, and analyzing mechanical systems.
Physics: Analyzing vectors, projectile motion, and wave phenomena.
Computer Graphics: Used in rendering, 2D and 3D modeling, and game development.
Surveying: Measuring distances and heights indirectly.
How this Calculator Works:
This calculator uses the Pythagorean theorem (a² + b² = c²) to find the hypotenuse (c) when the lengths of the two legs (a and b) are provided. It then calculates the area and perimeter based on these side lengths.
Example: If Side A is 3 units and Side B is 4 units: