How to Solve for Side A Using the Pythagorean Theorem with Sides 20 yd and 16 yd

The Pythagorean theorem is a fundamental principle in geometry that applies to right-angled triangles. It states:

a² + b² = c²

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

Given two sides of a right triangle, 20 yards and 16 yards, you can use this theorem to find the third side A. Here’s a step-by-step guide:

1. Identify the sides: Determine which sides are given and which one you want to find. Usually, if you’re solving for side A, check if 20 yards or 16 yards would likely be the hypotenuse.
2. Assumption 1 – If side A is the hypotenuse: Suppose 20 yd and 16 yd are the legs (sides a and b). Then:
• a = 20 yd
• b = 16 yd
• c = A (hypotenuse)
3. Write the Pythagorean formula:

A² = 20² + 16²

A² = 400 + 256 = 656

4. Take the square root:

A = √656 ≈ 25.61 yards

5. Assumption 2 – If side A is one of the legs: Suppose 20 yd is the hypotenuse, 16 yd is one leg, and A is the other leg.
• c = 20 yd
• b = 16 yd
• a = A
6. Use the formula:

A² + 16² = 20²

A² = 400 - 256 = 144

A = √144 = 12 yards

Summary:

• If A is the hypotenuse with legs 20 yd and 16 yd, then A ≈ 25.61 yd.
• If A is a leg, with hypotenuse 20 yd and other leg 16 yd, then A = 12 yd.

Make sure to clarify which side you are solving for (leg or hypotenuse) to apply the formula correctly.