Your kids have asked you to set up a cable fromtheir tree house to the ground
so that they can slide down quickly when it’s time to head in for lunch. The
tree house is 12 feet from the ground. You determine that in order to get a
gentle enough slope from the tree house to the ground, you need to anchor
the cable at least 35 feet from the base of the tree. How much cable will you
need to cover the distance from the tree house to the anchor point?
37 feet
A^2+b^2=c^2
12^ 2+35^2=c^2
144+1225=c^2
1369=c^2
Square root 1369 and c^2
C=37
To determine how much cable you will need to cover the distance from the tree house to the anchor point, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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.
In this case, the distance from the tree house to the anchor point forms the hypotenuse of a right triangle, with the vertical distance being 12 feet and the horizontal distance being 35 feet.
To find the length of the cable, we can use the Pythagorean theorem:
c^2 = a^2 + b^2
Where c is the length of the hypotenuse (or the cable in this case), and a and b are the lengths of the other two sides.
Plugging in the values, we get:
c^2 = 12^2 + 35^2
c^2 = 144 + 1225
c^2 = 1369
Taking the square root of both sides to find the length of the cable, we get:
c = sqrt(1369)
c ≈ 37 feet
Therefore, you will need approximately 37 feet of cable to cover the distance from the tree house to the anchor point.