How to Use the Pythagorean Theorem to Find Side A with Sides 50 m and 14 m

The Pythagorean theorem states that in a right-angled 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:

c² = a² + b²

Where c is the hypotenuse, and a and b are the other two sides.

Given two sides of lengths 50 meters and 14 meters, and you want to find side A (assuming it corresponds to one of the legs), you need to know which side is the hypotenuse. Let's consider two scenarios:

Scenario 1: You know 50 m and 14 m are the legs, find hypotenuse A

• Using the Pythagorean theorem:
  A² = 50² + 14²
  A² = 2500 + 196
  A² = 2696
• Now take the square root to find A:
  A = √2696 ≈ 51.92 meters

Scenario 2: You know hypotenuse is 50 m, one leg is 14 m, find other leg A

• Using the Pythagorean theorem:
  50² = A² + 14²
  2500 = A² + 196
  A² = 2500 - 196 = 2304
• Now take the square root to find A:
  A = √2304 = 48 meters

Summary: You must know which side is the hypotenuse to correctly apply the theorem:

• If both 50 m and 14 m are legs, hypotenuse (A) ≈ 51.92 m.
• If 50 m is the hypotenuse and 14 m is a leg, other leg (A) = 48 m.