# Right Triangle Calculator

## How to use the Right Triangle Calculator?

A triangle has three sides, meaning three vertices. A vertex is a point where two sides intersect. In a triangle, three vertices are joined by three independent segments, hence the edges. So a triangle with vertices a, b, and c.

The triangles are described by their length and internal angles. Now, if a triangle has three sides, it has equal lengths. It becomes an Equilateral triangle. #### What are the triangle facts?

• A triangle cannot have more than one vertex when an internal angle is equal to or greater than 90°. In such cases, it is not considered a triangle.
• The interior angle adds up to 180°. At the same time, the exterior angles are equal to the sum of two internal angles. They are not adjacent to it.
• Another way to calculate the exterior angle is to minus the angle of the vertex of interest from 180°.

#### What is a Pythagorean theorem?

The Pythagorean theorem is specific to right-angle triangles.

For any right-angle triangle, the square of the hypotenuse length equals the sum of squares of lengths of two sides. It follows a rule that the sides must make it a right angle. While some other cases, such as 30°60°90° and 45°45°90° and 3,4, 5 these triangles facilitate the calculation.

Here a and b are two sides of a triangle, and c is the hypotenuse. The Pythagorean theorem can be written as:

a2 + b2 = c2.

Example: If a = 3, c = 5, now find b:

32 + b2 = 52

9 + b2 = 25

b2 = 16 => b = 4.

In other words, c=hypotenuse, and a and b will be the other sides of the triangle.

a2 + b2 = c2.

It is known as the Pythagorean equation. It was named after the Greek Philosopher Pythagoras. The formula is important because if sides of a triangle are known or given. The theorem can determine the lengths and angles if the other two sides' lengths and angles are given. So if the angle between the other sides of a right angle is given, the law of cosines reduces the Pythagorean Equation.

#### What is the Right Triangle?

Some triangles are based on internal angles. These can be classified as oblique or right angles. A right triangle is one in which one angle is 90°. It is denoted by two lines forming a square at the vertex, making it a right angle. The longest edge of a triangle is the opposite edge of the right angle. It is called the hypotenuse. So any triangle that is not a right angle can be classified as either an oblique triangle or an Obtuse or acute angle.

A right triangle, in simple terms, has an angle that measures 90°. The relation and equation with the sides and angles are determining factors of trigonometry.

#### Factors about the Right Angle Triangle

• A right-angle triangle is the opposite of the 90° angle. It is also the longest side, called the hypotenuse.
• The sides of a right-angle triangle are commonly referred to with variables as a, b, and c. So c is the hypotenuse, and a and b are shorter than c and make the other sides of the triangle.
• The angles are also represented with capital letters corresponding to side lengths A, B, and C for small variables a, b, and c, respectively.

#### Let's understand the calculator

It has all the Greek symbols α(Alpha) and β (beta), which are used to measure unknown angles. In the calculator, h means the height or altitude of the triangle. It is the length of the vertex of the right angle. It is the hypotenuse of the triangle.

The altitude divides the triangle into two smaller triangles. It will form triangles similar to the original one. So all sides of the right-angle triangle have lengths called integers. It is called a Pythagorean triangle.

In a similar type of triangle, The three sides are collectively called the Pythagorean triple. For example:3, 4, 5; 5, 12, 13; 8, and others.

Any triangle's area and perimeter are calculated the same way as any other triangle. The perimeter is the sum of three sides of the triangle. The area can be calculated with the following formula.

A =1/2ab =1/2ch

#### What is a special Right Angle triangle?

The first one is a 30° 60° 90° triangle.

It refers to the angle measurements like 30°60°90°. So in this type of triangle, the sides correspond to angles 30°60°90°. They follow a ratio of 1:√3:2.

So in this type of triangle, if any side is known, the length of other sides can be calculated using the ratio given above.

Consider this as an example the side value is five, corresponding to the angle of 60°. Now consider "a" as the length corresponding to a 30° angle. Let's consider "b" as the length corresponding to 60° and "c" as the length of 90°

The following are the angles:

30° 60° 90°

The ratio of the sides: is 1:√3:2.

Length of the sides: a:5:c

Now use the known ratios of the sides of the triangle.

a=b/√3 =5/√3

c=b×2/√3 =10/√3

Now, with the above equation, it is clear that knowing one side of a 30°60°90° triangle helps you find the length of any other sides respectively. Now with this type of triangle, you can calculate trigonometric function for multiple of π/6.

The second one is a 45°45°90° triangle.

The 45°45°90° is a bit different than the 30°60°90°, and it is called an isosceles right triangle. It also has two sides with equal lengths. It is a right-angle triangle in which the sides correspond to angles 45°45°90°

It follows the ratio 1:1:√2.

Similar to the 30°60°90 triangle. It is important to know one side's length. It will help you find the length of the other sides of the 45°45°90° triangle.

Angle:45°45°90°

Side ratio:1:1:√2

Length of sides: a: a:c

Given information: c=5

a =c√2=5√2

A 45°45°90° triangle can help calculate the trigonometric functions with a multiple of π/4.

Effortlessly solve right triangle problems and explore special triangles with the powerful Right Triangle Calculator, simplifying your geometric calculations.

### Q: How does a Right Angled Triangle Calculator Calculate?

A: A right-angle triangle has one angle which measures 90°; hence it is a special type of Triangle. The Right Angled Triangle Calculator has an inbuilt Pythagorean Theorem by which it calculates the other sides and angles of the right-angled Triangle.

### Q: Why are the steps a Right Angled Triangle use?

A: In the Right Angled Triangle Calculator, input the values. The Calculator will determine the values of the Side and angles of the Triangle. First, find the angle a and then b using the formula. One angle will be 90 degrees as it is a right-angled calculator.

### Are all sides of a right-angled Triangle equal?

A: No, all the sides of a right-angle triangle are not equal. The Hypotenuse is the largest Side of the Triangle. It is the sum of the other two sides of the Triangle.

### What is a special Right Angled Triangle?

A Special Right Angled triangle or 45°45°90° and 30°60°90°.This angle measures 90° while the other angles are 45°, respectively. They have a fixed ratio of their sides.

### Q: How does a Right Angled Triangle calculator work?

A: The Right Angled Triangle Calculator is designed in a special way to calculate the area, perimeter, and sides of the triangle.

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