Final answer:
The length of the 8-foot piece of metal from the ground to the point where it touches the wall is approximately 6.9 feet, found by applying the Pythagorean theorem and rounding to the nearest tenth.
Step-by-step explanation:
Understanding the Problem
We are given a scenario where an 8-foot piece of metal is leaning against a wall, and the base of the metal is 4 feet from the wall. We can use the Pythagorean theorem to solve this problem, as it represents a right triangle with the piece of metal as the hypotenuse and the distances from the wall and the ground as the two legs.
Solving the Problem
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
a² + b² = c²
Substituting the given values into the equation, we have:
4² + b² = 8²
Thus, 16 + b² = 64
Solving for b, we find:
b² = 64 - 16
b² = 48
Taking the square root of both sides:
b = √48
b ≈ 6.9 (rounded to the nearest tenth)
The length of the metal from the ground to the wall is approximately 6.9 feet when rounded to the nearest tenth.