There is a slide in the park that is 18 feet long. The ladder to the top of the slide is 7.5 feet long. If the ladder and the slide are perpendicular, what is d, the distance from the top of the slide to the ground? If necessary, round to the nearest tenth
To find the distance (d) from the top of the slide to the ground, we can use the Pythagorean theorem.
According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two legs (sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this case, the length of the slide is one leg of the right triangle, and the length of the ladder is the hypotenuse.
Applying the Pythagorean theorem:
d^2 + 18^2 = 7.5^2
Simplifying:
d^2 + 324 = 56.25
Subtracting 324 from both sides:
d^2 = 56.25 - 324
d^2 = -267.75
Since we cannot take the square root of a negative number, it means there is no real solution for d.
To find the distance from the top of the slide to the ground, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 other two sides.
In this case, the ladder is the hypotenuse, and the length of the ladder is given as 7.5 feet. The length of the slide is one of the other two sides, given as 18 feet. Let's call the distance from the top of the slide to the ground "d", which is the remaining side we need to find.
Using the Pythagorean theorem, we can write the equation:
7.5^2 = d^2 + 18^2
Simplifying, we get:
56.25 = d^2 + 324
Subtracting 324 from both sides, we get:
d^2 = 56.25 - 324
d^2 = -267.75
Taking the square root of both sides, we have:
d ≈ √(-267.75)
Since we cannot take the square root of a negative number when working with real numbers, it means that there is no real solution for d in this case.