Right Triangle with Degrees Calculator

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

What is a Right Triangle?

A right triangle is a three-sided polygon with one angle exactly equal to 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 appear in many real-world applications.

Key properties of right triangles:

One angle is exactly 90 degrees
The sum of all angles is 180 degrees
The hypotenuse is always the longest side
The Pythagorean theorem applies (a² + b² = c²)

Right triangles can be classified further based on their angles:

45-45-90 triangle: Isosceles right triangle with two equal angles of 45°
30-60-90 triangle: Triangle with angles of 30°, 60°, and 90°
Scalene right triangle: All angles are different

How to Use This Calculator

To use the right triangle with degrees calculator:

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

Input requirements:

At least two values must be provided
Angles must be between 0° and 180°
Sides must be positive numbers
The sum of angles must be 180°

Formulas Used

The calculator uses these fundamental trigonometric formulas for right triangles:

Pythagorean Theorem

a² + b² = c²

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

Trigonometric Ratios

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

Angle Calculation

θ = arctan(opposite/adjacent)

θ = arcsin(opposite/hypotenuse)

θ = arccos(adjacent/hypotenuse)

Worked Examples

Let's solve a right triangle where we know one leg is 3 units and the adjacent angle is 30°.

Given	Find	Calculation	Result
Leg a = 3	Angle B	tan(B) = opposite/adjacent = a/b	B ≈ 30°
Leg a = 3	Leg b	b = a / tan(B)	b ≈ 5.196
Leg a = 3, Leg b ≈ 5.196	Hypotenuse c	c = √(a² + b²)	c ≈ 5.831

This example demonstrates how to find all sides and angles when given one side and one angle.

Applications

Right triangles are used in many practical applications:

Construction and architecture
Navigation and surveying
Engineering design
Physics calculations
Computer graphics

Common right triangle problems:

Finding height of a building
Determining the length of a ladder
Calculating the distance across a room
Solving projectile motion problems

FAQ

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

A right triangle has one exactly 90° angle, while an acute triangle has all angles less than 90°. An obtuse triangle has one angle greater than 90°.

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

You can use the Pythagorean theorem (a² + b² = c²) where c is the longest side. If the equation holds true, the triangle is right-angled.

What are the special right triangles?

The 45-45-90 and 30-60-90 triangles are special right triangles with predictable side ratios. A 45-45-90 triangle has sides in the ratio 1:1:√2, while a 30-60-90 triangle has sides in the ratio 1:√3:2.

Can a right triangle have two right angles?

No, a triangle can only have one right angle because the sum of angles in any triangle must be exactly 180°. Two right angles would sum to 180°, leaving no angle for the third side.