Sheila is climbing on a ladder that is attached against the side of a jungle gym wall. She is 4 feet off the ground and is 3 feet from the base of the ladder, which is 15 feet from the wall. How high up the wall is the top of the ladder?The ladder is attached to the wall of the jungle gym at a height of feet.
Question
Sheila is climbing on a ladder that is attached against the side of a jungle gym wall. She is 4 feet off the ground and is 3 feet from the base of the ladder, which is 15 feet from the wall. How high up the wall is the top of the ladder?The ladder is attached to the wall of the jungle gym at a height of feet.
Solution
This problem can be solved using the Pythagorean theorem, which 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.
Here, the ladder acts as the hypotenuse, the distance from the base of the ladder to the wall acts as one side of the triangle, and the height of the ladder from the ground acts as the other side of the triangle.
Given:
- The length of the ladder (hypotenuse) = 15 feet
- The distance from the base of the ladder to the wall = 3 feet
- Sheila's height above the ground = 4 feet
We need to find the height of the wall where the ladder touches it (let's call it 'h').
According to the Pythagorean theorem:
(hypotenuse)^2 = (side1)^2 + (side2)^2
So,
(15)^2 = (3)^2 + (h)^2
Solving this equation will give us the value of 'h'.
225 = 9 + h^2
Subtract 9 from both sides:
216 = h^2
Take the square root of both sides to solve for h:
h = √216
h = 14.7 feet
So, the top of the ladder is approximately 14.7 feet high on the wall.
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