Missing Side of a Right Triangle Calculator
Calculate missing sides and angles of a right triangle using the Pythagorean theorem
Calculate Missing Side
The longest side opposite to the right angle
Enter either side A or side B (not both)
Triangle Results
Enter the required values to calculate the missing side
Example Calculation
Find the Missing Side
Given: Right triangle with sides 9 cm and 12 cm
Find: The third side (hypotenuse)
Solution:
Using the Pythagorean theorem: c² = a² + b²
c² = 9² + 12² = 81 + 144 = 225
c = √225 = 15 cm
Calculate Angles
Angle α = arcsin(9/15) = 36.87°
Angle β = arcsin(12/15) = 53.13°
Right angle = 90°
Verification: 36.87° + 53.13° + 90° = 180° ✓
Right Triangle Diagram
a, b: Legs (perpendicular sides)
c: Hypotenuse (longest side)
α, β: Acute angles
90°: Right angle
Pythagorean Theorem
a = √(c² - b²)
b = √(c² - a²)
c = √(a² + b²)
Quick Tips
The hypotenuse is always the longest side
The right angle is always 90°
The sum of all angles equals 180°
Use trigonometry to find angles
Understanding Right Triangles and the Pythagorean Theorem
What is a Right Triangle?
A right triangle is a triangle that has one angle measuring exactly 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and it's always the longest side. The other two sides are called legs.
Properties of Right Triangles
- •One angle is exactly 90°
- •The other two angles are acute (less than 90°)
- •The sum of all angles is 180°
- •The hypotenuse is opposite the right angle
The Pythagorean Theorem
a² + b² = c²
This fundamental theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.
Applications
- •Construction and architecture
- •Navigation and GPS systems
- •Computer graphics and game development
- •Physics and engineering calculations