Pythagorean Theorem

Right Triangles

• A right triangle, or right-angled triangle, is a triangle in which one of the corners has an angle of 90^o
• For example:
• To show that it is a 90^o 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