To find the length of the third side of a triangle when you have two sides, you can use the Pythagorean theorem if the triangle is a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Example 1:
Given a = 9 and b = 12, to find c:
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
c^2 = 9^2 + 12^2
c^2 = 81 + 144
c^2 = 225
c = √225
c = 15
Therefore, in this case, c = 15.
Example 2:
Given a = 6 and b = 8, to find c:
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
c^2 = 6^2 + 8^2
c^2 = 36 + 64
c^2 = 100
c = √100
c = 10
Therefore, in this case, c = 10.