Right Triangle Calculator with Degrees

A right triangle is a triangle with one 90-degree angle. This calculator helps you determine the missing sides and angles when you know at least two values in a right triangle, including degree measurements.

What is a Right Triangle?

A right triangle is a polygon with three straight sides where one angle is exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. Right triangles are fundamental in geometry and trigonometry.

Key properties of right triangles:

One angle is exactly 90 degrees
The sum of all interior angles is 180 degrees
The Pythagorean theorem applies (a² + b² = c²)
Trigonometric functions (sine, cosine, tangent) can be used to find missing sides and angles

How to Use This Calculator

To use this right triangle calculator with degrees:

Enter two known values (sides or angles)
Select the units for each measurement
Click "Calculate" to see the results
Review the calculated values and chart visualization
Use the "Reset" button to clear all fields

Note: You must provide at least two values to get accurate results. The calculator will use trigonometric functions to determine the missing values.

Formulas Used

The calculator uses these fundamental formulas for right triangles:

Pythagorean Theorem

a² + b² = c²

Where c is the hypotenuse, and a and b are the legs

Trigonometric Functions

sin(θ) = opposite/hypotenuse

cos(θ) = adjacent/hypotenuse

tan(θ) = opposite/adjacent

Area of Right Triangle

Area = (base × height) / 2

Perimeter of Right Triangle

Perimeter = a + b + c

Worked Examples

Example 1: Find the Hypotenuse

Given legs of 3 units and 4 units, find the hypotenuse:

Using the Pythagorean theorem: √(3² + 4²) = √(9 + 16) = √25 = 5 units

Example 2: Find an Angle

Given legs of 1 unit and 1 unit, find the acute angles:

Using tan(θ) = opposite/adjacent = 1/1 = 1 → θ = arctan(1) = 45 degrees

Example 3: Find a Missing Leg

Given hypotenuse of 5 units and one leg of 3 units, find the other leg:

Using the Pythagorean theorem: √(5² - 3²) = √(25 - 9) = √16 = 4 units

Frequently Asked Questions

What is the difference between a right triangle and an acute triangle?

A right triangle has one 90-degree angle, while an acute triangle has all angles less than 90 degrees. Right triangles are a specific case of acute triangles.

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.

What if I only know one side of the triangle?

You need at least two known values to solve a right triangle. The calculator will show an error if you provide only one value.

How accurate are the degree measurements?

The calculator uses JavaScript's Math functions which provide accurate degree measurements to several decimal places.