>Hello Sohib EditorOnline, are you curious about how to find Pythagoras? In this article, we will discuss different methods to find the Pythagorean theorem.

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## What is Pythagorean Theorem?

Pythagorean Theorem is a formula in Mathematics to find the length of the sides of a right-angled triangle. The formula states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

### Example:

Suppose we have a right-angled triangle with sides a, b, and c. The length of side c is the hypotenuse. The formula to find the length of the hypotenuse is:

c^{2} = a^{2} + b^{2}

For example, if you know the length of sides a and b, you can use the formula to find the length of side c.

## Method 1: Using the Formula

The most common method to find the Pythagorean Theorem is to use the formula. There are different ways to use this formula.

### Formula with Sides a and b:

You can use the formula to find the length of the hypotenuse c if you know the length of sides a and b. The formula is:

c^{2} = a^{2} + b^{2}

Let’s say that a = 3 cm and b = 4 cm, then the length of c can be found by substituting the values in the formula:

c^{2} = 3^{2} + 4^{2}

c^{2} = 9 + 16

c^{2} = 25

c = √25

c = 5 cm

### Formula with Sides a and c:

You can also use the formula to find the length of side b if you know the length of sides a and c. The formula is:

b^{2} = c^{2} – a^{2}

Let’s say that a = 3 cm and c = 5 cm, then the length of b can be found by substituting the values in the formula:

b^{2} = 5^{2} – 3^{2}

b^{2} = 25 – 9

b^{2} = 16

b = √16

b = 4 cm

### Formula with Sides b and c:

Similarly, you can use the formula to find the length of side a if you know the length of sides b and c. The formula is:

a^{2} = c^{2} – b^{2}

Let’s say that b = 4 cm and c = 5 cm, then the length of a can be found by substituting the values in the formula:

a^{2} = 5^{2} – 4^{2}

a^{2} = 25 – 16

a^{2} = 9

a = √9

a = 3 cm

## Method 2: Using the Pythagorean Triplets

Another method to find the Pythagorean Theorem is to use Pythagorean Triplets. Pythagorean Triplets are sets of three positive integers that satisfy the Pythagorean Theorem. The most common Pythagorean Triplets are:

3 | 4 | 5 |

5 | 12 | 13 |

8 | 15 | 17 |

### Example:

Suppose we have a right-angled triangle with two sides that are multiples of a Pythagorean Triplet. For example, if one side is 3 cm and the other is 4 cm, we can use the Pythagorean Triplet (3, 4, 5) to find the length of the hypotenuse.

The Pythagorean Theorem states that:

c^{2} = a^{2} + b^{2}

Substituting the values, we get:

c^{2} = 3^{2} + 4^{2}

c^{2} = 9 + 16

c^{2} = 25

c = √25

c = 5 cm

## Method 3: Using Trigonometry

Trigonometry is another method to find the Pythagorean Theorem. You can use the trigonometric functions sine, cosine, and tangent to find the length of the sides of a right-angled triangle.

### Example:

Suppose we have a right-angled triangle with an angle of 30 degrees, and one side is 3 cm. We can use the trigonometric function sine to find the length of the hypotenuse.

The formula for sine is:

sin(θ) = opposite / hypotenuse

Substituting the values, we get:

sin(30) = 3 / c

c = 3 / sin(30)

c = 6 cm

## FAQ

### 1. What is the Pythagorean Theorem?

The Pythagorean Theorem is a formula in Mathematics to find the length of the sides of a right-angled triangle.

### 2. What is a right-angled triangle?

A right-angled triangle is a triangle with one angle that measures 90 degrees.

### 3. What are Pythagorean Triplets?

Pythagorean Triplets are sets of three positive integers that satisfy the Pythagorean Theorem.

### 4. What is Trigonometry?

Trigonometry is a branch of Mathematics that deals with the study of triangles and their properties.

### 5. What is the formula for the Pythagorean Theorem?

The formula for the Pythagorean Theorem is c^{2} = a^{2} + b^{2}.

### 6. Can I use the Pythagorean Theorem to find the length of any triangle?

No, the Pythagorean Theorem can only be used to find the length of the sides of a right-angled triangle.

### 7. Is Trigonometry difficult to learn?

Trigonometry can be difficult to learn, but with practice and dedication, anyone can master it.

### 8. Can I use the Pythagorean Theorem to find the area of a triangle?

No, the Pythagorean Theorem can only be used to find the length of the sides of a right-angled triangle. To find the area of a triangle, you need to use a different formula.

### 9. Are there any shortcuts to finding the Pythagorean Theorem?

Yes, you can use Pythagorean Triplets or Trigonometry to find the Pythagorean Theorem.

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

A triangle is right-angled if it has one angle that measures 90 degrees.

In conclusion, the Pythagorean Theorem is an important mathematical concept that is widely used in various fields. There are different methods to find the Pythagorean Theorem, including using the formula, Pythagorean Triplets, and Trigonometry. By understanding the Pythagorean Theorem, you can solve various problems and equations related to triangles.