Right Triangle Degrees Calculator

This right triangle degrees calculator helps you determine the angles of a right triangle when you know two sides or one angle. Right 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 triangle, follow these steps:

Enter the known values for two sides or one angle in the calculator form.
Click the "Calculate" button to compute the missing angles.
Review the results, which will show you the measures of all three angles in degrees.

The calculator will automatically determine which angles to calculate based on the values you provide. For example, if you know the lengths of all three sides, it will calculate all three angles. If you know one angle and one side, it will calculate the other angles.

Formula Explained

In a right triangle, the sum of the angles is always 180 degrees. The right angle is 90 degrees, so the other two angles must add up to 90 degrees. The relationship between the angles and sides is described by trigonometric functions:

sin(θ) = opposite/hypotenuse cos(θ) = adjacent/hypotenuse tan(θ) = opposite/adjacent

Where θ is one of the non-right angles, and the sides are labeled relative to θ. The calculator uses these relationships to determine the missing angles when given two sides or one angle.

Worked Examples

Example 1: Two Sides Known

Suppose you have a right triangle with sides of 3 units and 4 units. The hypotenuse can be calculated using the Pythagorean theorem:

hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5 units

Now, to find the angles:

Angle opposite to 3-unit side = arcsin(3/5) ≈ 36.87° Angle opposite to 4-unit side = arccos(4/5) ≈ 53.13°

The right angle is 90°, so the other two angles add up to 90° (36.87° + 53.13° ≈ 90°).

Example 2: One Angle and One Side Known

Suppose you know one angle is 30° and the side opposite to it is 2 units. You can find the hypotenuse using the sine function:

hypotenuse = 2 / sin(30°) = 2 / 0.5 = 4 units

Now, the other non-right angle is:

90° - 30° = 60°

So the angles are 30°, 60°, and 90°.

Frequently Asked Questions

What is a right triangle?

A right triangle is a triangle with one angle equal to 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs.

How do I know if a triangle is right-angled?

You can use the Pythagorean theorem: if a² + b² = c² (where c is the longest side), then the triangle is right-angled.

Can I use this calculator for non-right triangles?

No, this calculator is specifically designed for right triangles. For other types of triangles, you would need a different calculator.