How to Solve for Side 'A' Using the Pythagorean Theorem with Sides 50yd and 40yd

Step-by-step guide to finding the length of side A using the Pythagorean theorem when given two sides measuring 50 yards and 40 yards.

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

a² + b² = c²

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

Assuming you have two sides of a right triangle measuring 50 yards and 40 yards, and you want to solve for side A, here are the steps:

  1. Identify the sides: Let's say side A is one of the legs, and the other given side is 40 yards.
  2. Assuming the hypotenuse is 50 yards: This is typical since 50 is greater than 40, so 50yd is the hypotenuse c.
  3. Apply the formula: a² + b² = c², where a = A (unknown), b = 40 yards, c = 50 yards.
  4. Substitute the known values:

    5. A² + (40)² = (50)²

    A² + 1600 = 2500

  5. Isolate A²:

    6. A² = 2500 - 1600

    A² = 900

  6. Find A by taking the square root:

    7. A = √900

    A = 30 yards

Conclusion: The length of side A is 30 yards.

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