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.