Right Triangle Calculator
Solve a right triangle from its two legs.
Find the hypotenuse, area and angles of a right triangle.
How the Math Works
The Right Triangle Calculator uses the Pythagorean theorem to determine the hypotenuse (c) of a right triangle when given the lengths of the two legs (a and b). The formula c = √(a² + b²) calculates the longest side by squaring both legs, summing them, and taking the square root. Additionally, it applies the arctangent function (atan) to find the angle opposite one leg relative to the other, using the ratio a/b. These formulas allow precise computation of all sides and angles once two legs are provided, leveraging fundamental trigonometric and geometric principles.
Practical Applications
This calculator is invaluable in construction and engineering for tasks like determining rafter lengths in roofing or calculating distances between points with perpendicular offsets. For example, if a carpenter knows the horizontal and vertical distances of a roof ridge, the hypotenuse formula provides the exact rafter length needed. Similarly, in surveying, measuring two sides of a right triangle (e.g., ground distance and elevation change) lets professionals compute the direct slope distance and angle of incline quickly and accurately.
Day-to-Day Use
In everyday scenarios, this tool simplifies tasks requiring precise measurements or angles, such as setting up furniture at optimal angles, hanging pictures with level diagonals, or designing garden layouts with right-angled paths. Outdoor enthusiasts might use it to calculate hiking trail gradients or determine the safest ladder placement angle against a wall. Even in sports like basketball or soccer, understanding angles and distances via right triangles can improve shot accuracy or strategy planning.
Worked example
Legs 3, 4 → hypotenuse 5, area 6.
FAQ
Other angle?
The two non-right angles add to 90°.