To find the third side of a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is:
c² = a² + b²
Where:
– c is the length of the hypotenuse.
– a and b are the lengths of the other two sides.
If you know the lengths of two sides, you can easily find the third side by rearranging the formula. For example, if you know the lengths of sides a and b, you can find the hypotenuse c by taking the square root of the sum of a² and b².
Example:
Suppose you have a right triangle with sides a = 3 units and b = 4 units. To find the hypotenuse c:
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = √25
c = 5 units
So, the length of the hypotenuse is 5 units.
If you need to find one of the other sides (a or b) and you know the hypotenuse and the other side, you can rearrange the formula accordingly. For example, to find side a when you know sides b and c:
a² = c² – b²
a = √(c² – b²)
This method allows you to find the third side of any right triangle as long as you know the lengths of the other two sides.