Right Angle Triangle Degrees Calculator

This calculator helps you determine the angles of a right angle triangle when you know the lengths of two sides. Right angle triangles are fundamental in geometry and appear in many practical applications, from construction to navigation.

How to Use This Calculator

To calculate the angles of a right angle triangle:

Enter the length of the first side (adjacent to one angle)
Enter the length of the second side (opposite to one angle)
Click "Calculate" to see the results

The calculator will display the two non-right angles of the triangle in degrees. The right angle is always 90 degrees.

Note: The side you enter as "adjacent" will be opposite to the angle you're calculating, and vice versa. Make sure to label your sides correctly for accurate results.

Formula Explained

For a right angle triangle with sides a and b, and right angle C (90°), the other two angles A and B can be calculated using trigonometric functions:

tan(A) = opposite/adjacent = b/a

A = arctan(b/a)

B = 90° - A

Where:

A is the angle opposite side a
B is the angle opposite side b
a is the length of the side adjacent to angle A
b is the length of the side opposite to angle A

The calculator uses these formulas to compute the angles when you provide the side lengths.

Worked Examples

Example 1: Basic Triangle

Given a right angle triangle with sides 3 units (adjacent) and 4 units (opposite):

tan(A) = 4/3 ≈ 1.333

A ≈ arctan(1.333) ≈ 53.13°

B ≈ 90° - 53.13° ≈ 36.87°

This is a classic 3-4-5 triangle where the angles are approximately 53.13°, 36.87°, and 90°.

Example 2: Practical Application

If you're measuring a ramp that's 10 meters long and rises 2 meters vertically:

tan(A) = 2/10 = 0.2

A ≈ arctan(0.2) ≈ 11.31°

B ≈ 90° - 11.31° ≈ 78.69°

The ramp makes an angle of approximately 11.31° with the ground.

Frequently Asked Questions

What is a right angle triangle?: A right angle triangle is a triangle with one angle exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs.
How do I know which side is adjacent and which is opposite?: The side you're measuring the angle from is adjacent, and the side opposite to that angle is opposite. For example, if you're calculating angle A, side a is adjacent and side b is opposite.
Can I use this calculator for non-right triangles?: No, this calculator is specifically designed for right angle triangles. For other types of triangles, you would need a different calculator.
What if I enter zero for a side length?: The calculator will show an error message since a side length of zero doesn't form a valid triangle. Please enter positive numbers for both side lengths.
Is there a mobile app version of this calculator?: Currently, this calculator is available only as a web application. We don't have a dedicated mobile app, but you can access it from any device with a web browser.