Hypotenuse Calculator
Hypotenuse (Side c): 5.00
Area of Triangle: 6.00
Angle A: 36.9° | Angle B: 53.1°
Calculation Steps:
Learn More About the Hypotenuse
A hypotenuse calculator is a helpful tool for finding the longest side of a right-angled triangle. This longest side, called the hypotenuse, is always opposite the right angle (the 90° corner). Our interactive right triangle calculator uses the famous Pythagorean theorem formula (a² + b² = c²) to find the hypotenuse instantly. It's a great triangle calculator for students to check homework, and for teachers to demonstrate this key geometry concept visually.
This tool makes finding the hypotenuse easy by showing you the steps. Here's how to find the hypotenuse of a triangle with two sides using our tool:
- Input the lengths: You enter the lengths of the two shorter sides, 'a' and 'b'.
- Square the sides: The calculator squares each number (multiplies it by itself).
- Add them together: It then adds the two squared results.
- Find the square root: Finally, it calculates the square root of the sum. The result is the length of the hypotenuse, 'c'.
This hypotenuse calculator with steps and a square root display makes the entire process clear and easy to follow.
- Visual Demonstration: Use a projector to show how the triangle's shape and hypotenuse length change in real-time as you adjust the side lengths.
- Problem Solving: Give students word problems (e.g., "A ladder is leaning against a wall...") and have them use the tool to find the missing side and visualize the scenario.
- Discovery Learning: Let students play with the calculator to discover relationships, such as what happens when side 'a' and side 'b' are equal.
- Check for Understanding: After teaching the formula, allow students to use the calculator to check their own work.
Children are typically introduced to the Pythagorean theorem and the concept of a hypotenuse in middle school, around grades 6 through 8. While K-5 students focus on basic shapes and measurements, this tool's visual nature can serve as an early, engaging introduction to more advanced geometric ideas they will encounter later.
Example 1: The 3-4-5 Triangle
A classic example. If you enter Side a = 3 and Side b = 4, the calculator will show:
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
c = √25 = 5
The hypotenuse is 5.
Example 2: Finding a Missing Side
Let's say Side a = 5 and Side b = 12. The tool will calculate:
a² + b² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
c = √169 = 13
The hypotenuse is 13.
Educational Standards Alignment
This tool supports the following educational standards:
Common Core State Standards (CCSS):- 8.G.B.7: Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems.
- 7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
- MS-ETS1-1: Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution.
- MS-PS2-2: Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object (relates to vector components).
