Solve The Right Triangle Abc with C 90 Degrees Calculator

This calculator helps you solve right triangles where angle C is 90 degrees. Whether you know two sides or one side and an angle, you can find all missing sides and angles using the Pythagorean theorem and trigonometric ratios.

Introduction

A right triangle is a triangle with one 90-degree angle. In triangle ABC with angle C at 90 degrees, side c is the hypotenuse (the side opposite the right angle), and sides a and b are the legs. This calculator helps you find all sides and angles when you know at least two values.

Right triangles are fundamental in geometry and appear in many real-world applications, from construction to navigation. Understanding how to solve them is essential for many mathematical and practical problems.

How to Use This Calculator

Enter the known values for your right triangle. You can provide two sides or one side and one angle.
Select the units if applicable (degrees or radians for angles).
Click "Calculate" to find all missing sides and angles.
Review the results and the step-by-step solution.
Use the chart to visualize the triangle if needed.

Note: For best results, provide two known values. If you only provide one value, the calculator will assume the other is the hypotenuse.

Right Triangle Basics

In a right triangle ABC with angle C = 90 degrees:

Side c is the hypotenuse (opposite the right angle)
Sides a and b are the legs (opposite angles A and B)
The sum of angles A and B is 90 degrees

The Pythagorean theorem relates the sides of a right triangle: a² + b² = c².

Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

a² + b² = c²

This theorem is fundamental for solving right triangles when you know two sides.

Trigonometric Ratios

For any angle in a right triangle, you can find the ratios of the sides:

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

These ratios allow you to find angles when you know the sides.

Example Calculation

Let's solve a right triangle where side a = 3 units and angle A = 30 degrees.

First, find side b using the tangent function:
tan(30°) = b / a b = a * tan(30°) = 3 * 0.577 ≈ 1.732 units
Next, find the hypotenuse c using the Pythagorean theorem:
c = √(a² + b²) = √(9 + 3) ≈ √12 ≈ 3.464 units
Finally, find angle B:
angle B = 90° - angle A = 60°

This gives us a complete solution for the right triangle.

Frequently Asked Questions

What is a right triangle?: A right triangle is a triangle with one 90-degree angle. The side opposite the right angle is called the hypotenuse.
How do I solve a right triangle?: You can solve a right triangle using the Pythagorean theorem (when you know two sides) or trigonometric ratios (when you know a side and an angle).
What are the trigonometric ratios?: The trigonometric ratios are sine, cosine, and tangent, which relate the sides of a right triangle to its angles.
Can I solve a right triangle with only one known value?: No, you need at least two known values (two sides or one side and one angle) to solve a right triangle.
What is the hypotenuse?: The hypotenuse is the side opposite the right angle in a right triangle. It is the longest side.