Right Angled Triangle Calculator Degrees

This calculator helps you solve right-angled triangles where you know two values (sides or angles) and need to find the third. All calculations are done in degrees, making it perfect for geometry problems, construction measurements, and trigonometry practice.

How to Use This Calculator

To use the right-angled triangle calculator:

Enter two known values (either sides or angles)
Select the units for each measurement
Click "Calculate" to see the results
Review the solution and chart visualization

The calculator will automatically determine which values to solve for based on your inputs. For example, if you enter two sides, it will calculate the angles, and vice versa.

Formulas Used

This calculator uses fundamental trigonometric relationships for right-angled triangles:

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

Where θ is one of the non-right angles in degrees. The calculator automatically selects the appropriate formula based on which values you provide.

Worked Examples

Example 1: Find the Missing Side

Given a right-angled triangle with one angle of 30° and the hypotenuse of 10 units, we can find the opposite side:

opposite = hypotenuse × sin(30°) = 10 × 0.5 = 5 units

Example 2: Find the Missing Angle

Given a right-angled triangle with sides of 3 units (opposite) and 4 units (adjacent), we can find the angle θ:

tan(θ) = opposite/adjacent = 3/4
θ = arctan(3/4) ≈ 36.87°

These examples demonstrate how the calculator applies the trigonometric relationships to solve for unknown values.

Frequently Asked Questions

What is a right-angled triangle?: A right-angled 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.
Can I use this calculator for non-right-angled triangles?: No, this calculator is specifically designed for right-angled triangles. For other triangle types, you would need a different calculator.
What if I enter invalid values?: The calculator will show an error message if the values you enter create an impossible triangle (for example, if the sum of two angles is less than 90 degrees).
How accurate are the calculations?: The calculator uses JavaScript's built-in trigonometric functions, which provide accurate results to about 15 decimal places.
Can I use this calculator for real-world measurements?: Yes, this calculator is perfect for real-world applications like construction, engineering, and geometry problems where you need to work with right-angled triangles.