45°-45°-90° Triangle
Ratio: 1 : 1 : √2
Formula: c = a × √2
What is a 45-45-90 Triangle?
A 45-45-90 triangle is a special right triangle that has angles of 45°, 45°, and 90°. Because the two angles are equal, the opposite sides (called legs) are also equal in length.
This triangle is also known as an isosceles right triangle. It is one of the most important triangles in geometry because all of its sides follow a fixed ratio, allowing you to calculate unknown values instantly.
✔ A 45-45-90 triangle can be solved instantly using the ratio 1 : 1 : √2.
👉 If one side is known, all other sides, area, and perimeter can be calculated easily.
45-45-90 Triangle Formula
In a 45-45-90 triangle, all sides follow a constant ratio:
- Leg a = Leg b (both sides are equal)
- Hypotenuse (c) = a × √2
- Leg (a) = c ÷ √2
Additional Formulas
- Area = a² / 2
- Perimeter = a(2 + √2)
👉 These formulas come from the Pythagorean theorem (a² + b² = c²).
Why is it Important?
- Used in geometry and trigonometry
- Helpful in engineering and construction
- Quick calculations without complex formulas
How to Use This Calculator?
- Select known side (leg or hypotenuse)
- Enter value
- Click calculate
- View instant result and triangle
How to Solve a 45-45-90 Triangle?
- If leg is known → multiply by √2 to find hypotenuse
- If hypotenuse is known → divide by √2 to find leg
- Use area = a² / 2
- Use perimeter = a(2 + √2)
FAQ on 45-45-90 triangle
A triangle with angles 45°, 45°, and 90° where both legs are equal.
Hypotenuse = Leg × √2 and Leg = Hypotenuse ÷ √2.
The ratio is 1 : 1 : √2.