Answer:
Explanation:
Let's call the distance from the tower's base to the end of the wire "d". According to the problem, the height of the tower is 8 feet greater than "d". We can write this as:
height of tower = d + 8
We also know that the wire is 40 feet long. The wire stretches from the ground to the top of the tower, so we can use the Pythagorean theorem to relate the distance "d", the height of the tower, and the length of the wire:
d^2 + (d + 8)^2 = 40^2
Expanding and simplifying this equation gives:
2d^2 + 16d - 960 = 0
Dividing both sides by 2 gives:
d^2 + 8d - 480 = 0
We can solve this quadratic equation using the quadratic formula:
d = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 8, and c = -480. Substituting these values and simplifying, we get:
d = (-8 ± sqrt(8^2 + 4(480))) / 2
d = (-8 ± sqrt(2080)) / 2
d ≈ -25.73 or d ≈ 17.73
Since "d" represents a distance, it cannot be negative. Therefore, we choose the positive solution:
d ≈ 17.73
Now we can use the equation we derived earlier to find the height of the tower:
height of tower = d + 8
height of tower ≈ 17.73 + 8
height of tower ≈ 25.73
So the distance from the tower's base to the end of the wire is approximately 17.73 feet, and the height of the tower is approximately 25.73 feet.