Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide. How far is the bottom of the ladder from the bottom of the slide?

Question

Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide. How far is the bottom of the ladder from the bottom of the slide?

Answer 1

Hello Delvin!

This problem can be represented by a right triangle. Since the ladder of the slide is vertical, we can assume it forms a right angle with the ground. The length of the slide is the hypotenuse of the triangle because it is the side opposite the right angle, and the distance between the end of the slide and the ladder is the third side.

Remember that the Pythagorean theorem states for any right triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. In this problem, the hypotenuse is 17, and we know the length of one other side, which is 8.

c = 17

a = 8

We can plug these numbers in to the Pythagorean theorem and solve for b.

8² + b² = 17²

64 + b² = 289 Here I squared 8 and 17

b² = 225 Here I subtracted 64 from both sides

b = ±15

Since b is a side length it cannot be negative, so b = 15.

The distance between the bottom of the ladder and the foot of the slide is 15 feet.

Good luck with your homework!

Katie

Answer 2

assuming the slide is not curved,

it is the hypotenuse of a right triangle

hypotenuse squared = sum of squares of the other two sides

17^2 = 15^2 + 8^2

289 = 225 + 64

15 feet

Answer 3

To find "x", use the Pythagorean Theorem (a² + b² = c²)

8² + x² = 17²

64 + x² = 289

x² = 225

x = √225 = 15

So the bottom of the ladder is 15 feet from the bottom of the slide.