45 45 90 Triangle Calculator
Solve a 45-45-90 right triangle from a leg.
An isosceles right triangle with a fixed side ratio 1 : 1 : √2.
How the Math Works
A 45-45-90 triangle is a special right triangle where the two legs are equal in length, and the angles are 45°, 45°, and 90°. The relationship between the legs and hypotenuse follows a consistent ratio of 1:1:√2. When given the length of one leg, the hypotenuse can be calculated by multiplying the leg length by √2 (approximately 1.414). This formula eliminates the need for complex trigonometric functions or the Pythagorean theorem, streamlining calculations for this specific triangle type.
Practical Applications
This calculator is invaluable in fields requiring precise diagonal measurements, such as construction, carpentry, or architecture. For example, when building a square frame, a carpenter can quickly determine the diagonal brace length by inputting the side length. It's also useful in geometry problems involving isosceles right triangles, allowing students and professionals to solve real-world scenarios like calculating roof rafter lengths or screen diagonals efficiently without manual computation.
Day-to-Day Use
In everyday life, this tool simplifies tasks that involve right angles and equal sides. Imagine setting up a tent with a square base or arranging furniture diagonally in a room — knowing the diagonal distance becomes straightforward. It also aids in sports and fitness, such as calculating the shortest path for a diagonal sprint on a field, or in crafting and DIY projects where accurate measurements prevent material waste and ensure structural integrity.
Worked example
Leg 5 → hypotenuse 7.07.
FAQ
Half a square?
Yes — it's a square cut along its diagonal.