How to Solve for B Using the Pythagorean Theorem with Given Sides 48yd and 64yd

The Pythagorean theorem is a mathematical formula used to find the length of a side in a right triangle. It states that:

a² + b² = c²

Here, c is the hypotenuse (the side opposite the right angle, and the longest side), and a and b are the other two sides.

Step 1: Identify the sides.

Suppose we are given two side lengths:

• One side = 48 yards
• Another side = 64 yards

We need to clarify which one is the hypotenuse (c) and which sides are a and b.

Typically, the longest side is the hypotenuse (c). Here, 64 yards is longer than 48 yards, so let’s consider:

• c = 64yd (hypotenuse)
• a = 48yd (one leg)
• b = unknown leg (we want to find this length)

Step 2: Apply the Pythagorean theorem formula:

a² + b² = c²

Substitute the known values:

(48)² + b² = (64)²

Calculate squares:

2304 + b² = 4096

Step 3: Solve for b²:

b² = 4096 - 2304

b² = 1792

Step 4: Find b by taking the square root:

b = √1792

Calculate √1792:

b ≈ 42.33 yards

Answer: The length of side B is approximately 42.33 yards.

Summary: Given sides 48 yards and 64 yards, assuming 64 yards is the hypotenuse, the missing side B is about 42.33 yards using the Pythagorean theorem.