The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It states that:
a² + b² = c²
Here, 'a' and 'b' are the lengths of the two legs (shorter sides), and 'c' is the length of the hypotenuse (the side opposite the right angle).
To solve for side A using the given sides 6.8 ft and 6.1 ft, you first need to determine what side 'A' represents. Assuming that 6.8 ft and 6.1 ft are the lengths of the two legs, then 'A' would be the hypotenuse 'c'.
Step-by-step calculation:
- Identify the sides:
a = 6.8 ft
b = 6.1 ft - Apply the theorem:
c² = a² + b² - Calculate squares:
6.8² = 46.24
6.1² = 37.21 - Add the squares:
46.24 + 37.21 = 83.45 - Find the square root to get side A (c):
c = √83.45 ≈ 9.14 ft
Answer: The length of side A is approximately 9.14 feet.
Note: If 'A' corresponds to a leg instead of the hypotenuse, or if the known sides are different, you would rearrange the formula accordingly.