Hypotenuse Calculator
Enter an adjacent side and an acute angle. Then calculate the hypotenuse instantly.
Example Data Table
These sample values show how angle and adjacent side determine the hypotenuse.
| Adjacent Side | Angle | Hypotenuse | Opposite Side |
|---|---|---|---|
| 5.00 | 30.00° | 5.7735 | 2.8868 |
| 8.00 | 35.00° | 9.7662 | 5.6017 |
| 10.00 | 45.00° | 14.1421 | 10.0000 |
| 12.00 | 60.00° | 24.0000 | 20.7846 |
| 15.00 | 25.00° | 16.5507 | 6.9946 |
Formula Used
Primary identity: cos(θ) = adjacent / hypotenuse
Rearranged formula: hypotenuse = adjacent / cos(θ)
Helpful extra: opposite = adjacent × tan(θ)
This method works for right triangles when the given angle is acute and the known side is adjacent to that angle.
How to Use This Calculator
- Enter the adjacent side length.
- Enter the acute angle value.
- Select degrees or radians.
- Choose the number of decimal places.
- Set a graph angle range in degrees.
- Click the calculate button.
- Review the result, steps, and graph.
- Use the export buttons for CSV or PDF files.
Frequently Asked Questions
1. What does this calculator find?
It finds the hypotenuse of a right triangle when you know an acute angle and the adjacent side. It also shows the opposite side and working steps.
2. Which formula does it use?
It uses cos(θ) = adjacent / hypotenuse. Rearranging gives hypotenuse = adjacent / cos(θ). That is the direct formula used in the calculation.
3. Can I use degrees or radians?
Yes. Choose the unit that matches your input. The calculator converts values internally so the trigonometric functions work correctly.
4. Why must the angle be less than 90 degrees?
This tool is for right triangles using an acute reference angle. Angles of 0 or 90 degrees do not produce a valid practical setup here.
5. Why does the hypotenuse grow quickly near 90 degrees?
As the angle rises, cosine gets smaller. Since the formula divides by cosine, the hypotenuse increases rapidly when the angle approaches 90 degrees.
6. What do the CSV and PDF buttons export?
They export the current calculation summary. The files include the adjacent side, angle, unit, cosine value, opposite side, and hypotenuse result.
7. What does the graph represent?
The graph plots angle against hypotenuse while keeping the adjacent side fixed. It helps you see how the longest side changes across the angle range.
8. Can this tool also show the opposite side?
Yes. It calculates the opposite side with adjacent × tan(θ). That extra value helps you understand the full triangle dimensions.