Answer:
Explanation:
To find the length of the wire supporting the tree, you can use the Pythagorean theorem because the tree, the wire, and the distance from the base of the tree to the anchor point form a right triangle.
Let:
- "h" be the height of the tree.
- "d" be the distance from the base of the tree to the anchor point.
- "w" be the length of the wire.
According to the problem, the wire is 8 feet longer than the height the tree reaches, so you can write:
w = h + 8
You're also given that the distance from the base of the tree to the anchor point is 12 feet:
d = 12
Now, you can use the Pythagorean theorem:
w^2 = h^2 + d^2
Substitute the expressions for w and d:
(h + 8)^2 = h^2 + 12^2
Expand and simplify:
h^2 + 16h + 64 = h^2 + 144
Now, subtract h^2 from both sides to isolate the variable "h":
16h + 64 = 144
Subtract 64 from both sides:
16h = 144 - 64
16h = 80
Now, divide by 16 to solve for h:
h = 80 / 16
h = 5
So, the height of the tree is 5 feet. Now that we know the height, we can find the length of the wire using the relationship w = h + 8:
w = 5 + 8
w = 13
The length of the wire is 13 feet.