# Pythagorean Theorem

### Pythagorean Theorem

#### Right Triangles

• A right triangle, or right-angled triangle, is a triangle in which one of the corners has an angle of 90o
• For example:
• To show that it is a 90o angle we add a little square in the corner: This is also called a 'right angle'
• The longest side of the triangle is always the one opposite the right angle. This side is called the 'hypotinuse':

#### Pythagorean theorem

• The pythagorean theorem can be used to find the length of the hypotinuse given the length of the other two sides.
• if a, b, and c are the length of the three sides:
• The pythagorean theorem states that:
``c2 = a2 + b2``

#### Example

• if a = 4 and b = 3, calculate the length of c
• Using the pythagorean theorem, we know that:
• Now we just solve for c:

#### Finding other sides

• We can also use the pythagorean theorem to find the length of any side, given that we know the other two.
• For example: if a = 8 and c = 10, calculate the length of b
• Using the pythagorean theorem, we know that:
• Now we solve for b:

#### code (Python)

``````import math

a = 4
b = 3
c = math.hypot(a, b)

print(c) # prints: 5``````