Final answer:
The equation is based on the Pythagorean theorem, suggesting a right-angled triangle with a hypotenuse of 8 units and one side of 7 units. By solving the equation, we find that the length of the other side, A, is approximately 3.87 units.
Step-by-step explanation:
The equation provided, 8² = A² + 7², is suggestive of the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c² = a² + b². Given the equation, we can observe that 8 is the hypotenuse (c), and 7 is one of the other sides (a or b), while A represents the length of the other side that we are looking to find. To solve for A, we rearrange the equation to A² = 8² - 7², and then we take the square root of both sides to find the length of side A.
Using the equation, we have:
- A² = 64 - 49
- A² = 15
- A = √15 ≈ 3.87
Thus, the missing side A is approximately 3.87 units long.