The Pythagorean Theorem is a fundamental principle in geometry useful for finding the length of a side in a right 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.
Given two sides of lengths 34 yards and 16 yards, and you want to find the third side 'B', here's how you can proceed step-by-step:
- Identify the sides: Determine which sides correspond to 'a', 'b', and 'c'. Typically, if you know the hypotenuse (the longest side), that will be 'c'.
- Assuming 34 yd is the hypotenuse (c): If 34 yd is the longest side, then:
- Apply the Pythagorean Theorem:
- Solve for b²:
- Find b:
- Solution: The missing side B is 30 yards.
c = 34 yd, one leg (a) = 16 yd, find the other leg (b) = ?
a² + b² = c²
Substitute the known values:
16² + b² = 34²
256 + b² = 1156
b² = 1156 - 256 = 900
b = √900 = 30 yd
Note: If the 34 yd is not the hypotenuse, and both 34 yd and 16 yd are legs, then B would be the hypotenuse:
B² = 34² + 16² = 1156 + 256 = 1412
B = √1412 ≈ 37.58 yd
So, always identify which side is the hypotenuse first before solving.