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:
a² + b² = c²
Here, let's assume you have two sides measuring 5 ft and 4 ft, and you want to solve for side B. Depending on which side B represents (either one of the legs or the hypotenuse), the method will vary:
Case 1: Finding the Hypotenuse (side C)
If the sides 5 ft and 4 ft are the two legs (a and b), then the hypotenuse c (side B in your case) can be found by:
c = √(a² + b²)
Substitute the known values:
c = √(5² + 4²) = √(25 + 16) = √41 ≈ 6.4 ft
Case 2: Finding a Leg (side B), when the hypotenuse and one leg are known
If you know the hypotenuse is 5 ft, and one leg is 4 ft, and you want to find the other leg B, then:
b = √(c² - a²)
Substitute the values:
b = √(5² - 4²) = √(25 - 16) = √9 = 3 ft
Summary
- If 5 ft and 4 ft are the legs, then to find the hypotenuse B: B = √(5² + 4²) ≈ 6.4 ft
- If 5 ft is the hypotenuse and 4 ft is one leg, then to find leg B: B = √(5² - 4²) = 3 ft
Make sure to identify which side you want to find and whether it is a leg or the hypotenuse.