How to Solve for Side A Using the Pythagorean Theorem with Sides 50m and 14m

The Pythagorean theorem relates the lengths of the sides of 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.

To solve for side A when you have sides of 50 meters and 14 meters, you need to know which side is the hypotenuse.

Case 1: If 50m is the hypotenuse (c), and 14m is one leg (b), find A (the other leg)

Use the formula:
A² + 14² = 50²

Calculate squares:
A² + 196 = 2500

Subtract 196 from both sides:
A² = 2500 - 196 = 2304

Take the square root:
A = √2304 = 48 meters

Case 2: If 50m and 14m are the legs (a and b), and you want to find the hypotenuse (A)

Use the formula:
50² + 14² = A²

Calculate squares:
2500 + 196 = A²

Sum:
2696 = A²

Take the square root:
A = √2696 ≈ 51.92 meters

Summary:
- If 50m is the hypotenuse, A = 48m
- If 50m and 14m are legs, hypotenuse A ≈ 51.92m