How to Use the Pythagorean Theorem to Find the Unknown Side B Given 5 ft and 4 ft

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.