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Right Triangle Calculator - Solve Right Triangles
Geometry & Trigonometry Tool

Right Triangle Calculator

Solve right triangles quickly by calculating missing sides, angles, area and perimeter from the measurements you already know.

Solve Your Right Triangle

Enter the measurements you know
Known Measurements a² + b² = c²
Enter leg a.
Enter leg b when using a + b.
Enter c when using a + c.
Angle Method sin(A) = a / c
Use side a opposite angle A.
Enter an acute angle in degrees.
Clear Calculator

What Is a Right Triangle Calculator?

A Right Triangle Calculator is a geometry and trigonometry tool designed to solve the missing measurements of a right triangle. A right triangle contains one angle measuring exactly 90 degrees.

The calculator can determine unknown side lengths, angles, area and perimeter when enough information is provided. It uses the Pythagorean theorem and basic trigonometric relationships to solve the triangle.

It is useful for students, teachers, engineers, construction professionals and anyone working with right-triangle measurements.

How to Use the Right Triangle Calculator

Choose the calculation method that matches the measurements you already know. Then enter the values and calculate the complete triangle.

1

Choose a Method

Select two known sides or a known side and an acute angle.

2

Enter Measurements

Enter the known side lengths and angles into the calculator.

3

Get the Solution

The calculator finds the missing sides, angles, area and perimeter.

Pythagorean Theorem for Right Triangles

The Pythagorean theorem is one of the most important relationships used to solve right triangles. It states that the square of the hypotenuse equals the sum of the squares of the two legs.

a² + b² = c²

If both legs are known, the hypotenuse can be found with:

c = √(a² + b²)

If the hypotenuse and one leg are known, the other leg can be calculated using:

b = √(c² − a²)

Trigonometric Ratios in a Right Triangle

When one side and an acute angle are known, trigonometric functions can be used to calculate the remaining sides.

sin(A) = opposite / hypotenuse

cos(A) = adjacent / hypotenuse

tan(A) = opposite / adjacent

These relationships allow you to solve a right triangle even when two side lengths are not known.

Right Triangle Example

Suppose a right triangle has legs of 3 and 4 units. The hypotenuse can be calculated using the Pythagorean theorem.

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = 5

The hypotenuse is therefore 5 units. The area is:

Area = ½ × 3 × 4

Area = 6 square units

The two acute angles are approximately 36.87° and 53.13°, while the third angle is exactly 90°.

Frequently Asked Questions

What is a right triangle?

A right triangle is a triangle containing one angle that measures exactly 90 degrees. The side opposite this angle is called the hypotenuse.

What is the formula for a right triangle?

The primary formula for finding side lengths is the Pythagorean theorem: a² + b² = c².

Which side is the hypotenuse?

The hypotenuse is always opposite the 90-degree angle and is the longest side of a right triangle.

Can this calculator find the missing side?

Yes. Enter two known sides and the calculator can determine the remaining side using the appropriate right-triangle formula.

Can I calculate a right triangle from an angle?

Yes. Enter one known side and an acute angle. The calculator uses sine, cosine and tangent relationships to determine the remaining measurements.

What is the area of a right triangle?

The area is calculated by multiplying the two perpendicular legs and dividing the result by two: Area = ½ab.

Do the angles of a right triangle add up to 180°?

Yes. One angle is 90 degrees, and the other two acute angles always add up to 90 degrees.

Can I enter decimal values?

Yes. The calculator accepts decimal side lengths and angle measurements for more precise calculations.

What units does the calculator use?

The calculator works with any consistent unit system. If your sides are in meters, the area will be in square meters and the perimeter will be in meters.