Final answer:
The height of the top of the slide with a 65-degree angle to the ground is approximately 10.2 feet, calculated using the sine function of trigonometry.
Step-by-step explanation:
The student is asking to estimate the height of the top of the slide when a 12-foot slide is attached to a swing set at a 65-degree angle. To solve this, we should use trigonometric functions, specifically the sine function, which relates the opposite side of a right triangle (the height of the slide, in this case) to the hypotenuse (the length of the slide).
To calculate the height (h), we use the formula: h = length of slide × sin(angle). Plugging in the values we get: h = 12 feet × sin(65 degrees). Using a calculator, sin(65 degrees) is approximately 0.9063. Thus, h = 12 × 0.9063 ≈ 10.876 feet.
The estimated height of the top of the slide is closest to option c) 10.2 feet.