Final answer:
After applying the Pythagorean theorem to the right-angled triangle formed by the slide's height and hypotenuse, the distance from the base to the end of the slide is approximately 8.49 feet, which after rounding would be 8 feet. The provided options do not match this calculation, indicating a possible mistake in the options.
Step-by-step explanation:
The Juneton City Council plans to install new slides at its playgrounds, and the question asks us to calculate how far the end of the slides will be from the base of the playground structure. Since the slides are 11 feet long and need to be mounted at least 7 feet up on the playground structure, we can use the Pythagorean theorem to solve this problem.
The slide forms the hypotenuse of a right-angled triangle, with its height being one side (7 feet) and the distance from the base of the playground structure to the end of the slide forming the other side.
We can denote the distance from the base as 'd', use the Pythagorean theorem which is a^2 + b^2 = c^2 where 'a' and 'b' are the sides of the triangle and 'c' is the hypotenuse.
The calculation will be:
- a = 7 feet (height)
- c = 11 feet (length of the slide, the hypotenuse)
We are looking for 'b', which is 'd' the distance from the base:
- 7^2 + d^2 = 11^2
- 49 + d^2 = 121
- d^2 = 121 - 49
- d^2 = 72
- d = √72
- d ≈ 8.49 feet
Since none of the given options are 8.49 feet, we round to the nearest whole number, which is 8 feet. The closest answer choice to 8 is option d) 5 feet, but this is not correct based on the calculation. It seems there might be a mistake with the options provided.