Final answer:
The horizontal distance from the bottom of the staircase to the bottom of the skateboard ramp is found using the Pythagorean theorem and is approximately 8.3 feet when rounded to the nearest tenth of a foot.
Step-by-step explanation:
The question asks us to find the horizontal distance from the bottom of the staircase to the bottom of a skateboard ramp, given the height of the ramp and the length of the staircase. This forms a right triangle, where the height of the ramp is one leg, the length of the staircase is the hypotenuse, and the horizontal distance from the bottom of the ramp is the other leg we are trying to find.
Using the Pythagorean theorem: a2 + b2 = c2, where 'c' is the length of the hypotenuse, 'a' is one leg, and 'b' is the other leg, we can solve for the horizontal distance (b).
Given: c (hypotenuse) = 15 feet and a (height of ramp) = 12.5 feet.
Solving for b:
b2 = c2 - a2
b2 = 152 - 12.52
b2 = 225 - 156.25
b2 = 68.75
b = √68.75
b ≈ 8.29 feet, which rounds to 8.3 feet when rounded to the nearest tenth of a foot.
Therefore, the correct answer is A) 8.3 feet.