Right Angled Triangle Degrees Calculator

This calculator helps you find the angles in a right-angled triangle using trigonometric functions. Whether you know two sides or one side and an angle, you can determine all angles in the triangle.

How to Use This Calculator

To use the right-angled triangle degrees calculator:

Enter the known values for the sides of the triangle (adjacent, opposite, or hypotenuse).
Select which angle you want to calculate (angle A, angle B, or angle C).
Click "Calculate" to see the results.
Review the calculated angles and the triangle visualization.

The calculator will display the angles in degrees and provide a visual representation of the triangle.

Formulas Used

Trigonometric Functions

For a right-angled triangle with sides a, b, and hypotenuse c:

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

These functions allow you to calculate angles when you know the sides.

Note: All angles in a triangle must add up to 180 degrees. The right angle is always 90 degrees.

Worked Examples

Example 1: Find Angle A

Given a right-angled triangle with opposite side = 3 and hypotenuse = 5:

sin(A) = opposite/hypotenuse = 3/5

A = arcsin(3/5) ≈ 36.87°

Example 2: Find Angle B

Given a right-angled triangle with adjacent side = 4 and hypotenuse = 5:

cos(B) = adjacent/hypotenuse = 4/5

B = arccos(4/5) ≈ 36.87°

Common Right-Angled Triangle Problems

This calculator can solve several common right-angled triangle problems:

Finding an angle when two sides are known
Determining the third angle when two angles are known
Verifying if a triangle is right-angled

The calculator provides quick and accurate solutions to these problems.

Frequently Asked Questions

What is a right-angled triangle?: A right-angled triangle is a triangle with one angle equal to 90 degrees. The side opposite the right angle is called the hypotenuse.
How do I calculate angles in a right-angled triangle?: You can use trigonometric functions (sine, cosine, tangent) to calculate angles when you know the sides. The calculator automates this process.
What if I don't know any angles or sides?: You need at least two pieces of information (two sides or one side and one angle) to calculate the angles in a right-angled triangle.
Can I use this calculator for non-right-angled triangles?: No, this calculator is specifically designed for right-angled triangles. For other types of triangles, you would need a different calculator.