Length of cable

Question

Eye hook 25ft high in tree

Eye hook base of other tree which is 18 ft away.

Answer 1

To find the length of the cable needed to connect an eye hook 25 feet high in one tree to an eye hook at the base of another tree 18 feet away, you can use the Pythagorean theorem. The setup forms a right triangle, with the height of the first tree and the horizontal distance between the trees as the two legs of the triangle.

The Pythagorean theorem states that:

c^2 = a^2 + b^2

where c is the length of the hypotenuse (the cable), a is the height of the eye hook in the first tree (25 feet), and b is the horizontal distance between the trees (18 feet).

Plugging in the values:

c^2 = 25^2 + 18^2

c^2 = 625 + 324

c^2 = 949

c = sqrt 949

approx 30.8

So, the length of the cable needed is approximately 30.8 feet.

Answer 2

Think of it like a triangle. Tree 1 is 25 feet high, a = 25. Tree 2 is 18 feet away, b = 18. Clearly, the cable that is attached from the top of Tree 1 to the base of Tree 2 is the hypotenuse of this triangle, c.

So, a^2 + b^2 = c^2, c = sqrt(a^2 + b^2)

Therefore, c = sqrt(25^2 + 18^2) = sqrt(949) = 30.81

So the cable is 30.81 feet long.