Cal11 calculator
Search calculator...

Hypotenuse Calculator Degrees

Reviewed by Calculator Editorial Team

This hypotenuse calculator helps you find the length of the hypotenuse in a right triangle when you know one side and one angle. Whether you're a student studying geometry or a professional working with technical drawings, this tool provides quick and accurate results.

What is the Hypotenuse?

In a right triangle, the hypotenuse is the side opposite the right angle and is the longest side of the triangle. It's named after the Greek word "hypoteinousa" meaning "to stretch under" or "to extend."

The hypotenuse plays a crucial role in trigonometric functions. The sine, cosine, and tangent functions are all defined in terms of the hypotenuse in a right triangle.

How to Calculate Hypotenuse with Degrees

Calculating the hypotenuse when you know one side and one angle involves using trigonometric functions. Here's a step-by-step guide:

  1. Identify the known side length and angle.
  2. Choose the appropriate trigonometric function based on which side you know:
    • If you know the adjacent side, use cosine.
    • If you know the opposite side, use sine.
  3. Apply the trigonometric function to the angle to find the ratio.
  4. Multiply the ratio by the known side length to find the hypotenuse.

Remember that the angle must be in degrees for this calculation. If your angle is in radians, you'll need to convert it first.

The Formula

The formula for calculating the hypotenuse when you know one side and one angle is:

hypotenuse = (known side) / (trig function of angle)

Where the trig function depends on which side you know:

  • If you know the adjacent side: hypotenuse = adjacent / cos(angle)
  • If you know the opposite side: hypotenuse = opposite / sin(angle)

Worked Example

Let's say you have a right triangle with an angle of 30 degrees and the side adjacent to that angle is 10 units long. Here's how to find the hypotenuse:

  1. Identify the known values: angle = 30°, adjacent side = 10 units
  2. Choose the appropriate trigonometric function: cosine (since we know the adjacent side)
  3. Calculate the cosine of 30 degrees: cos(30°) ≈ 0.8660
  4. Apply the formula: hypotenuse = 10 / 0.8660 ≈ 11.547 units

The hypotenuse of this right triangle is approximately 11.547 units.

Frequently Asked Questions

What is the difference between the hypotenuse and the legs of a right triangle?
The hypotenuse is the side opposite the right angle and is the longest side. The other two sides are called legs and are adjacent to the right angle.
Can I use this calculator for angles in radians?
No, this calculator only accepts angles in degrees. You'll need to convert your angle to degrees before using this tool.
What if I don't know either side but know the angle?
If you know the angle but not either side, you'll need additional information to calculate the hypotenuse. You could use the definition of sine or cosine with a known ratio.