Final answer:
Using trigonometry, the slide which is 10 ft long and 8 ft high makes an angle of approximately 53 degrees with the ground.
Step-by-step explanation:
To find the angle that the 10 ft slide makes with the ground when the top of the slide is 8 ft above the ground, we can use trigonometry, specifically the sine function which relates the angle to the ratio of the opposite side (height of the slide) over the hypotenuse (length of the slide).
The sine of the angle θ is equal to the height of the slide divided by the length of the slide:
sin(θ) = opposite / hypotenuse
sin(θ) = 8 ft / 10 ft
sin(θ) = 0.8
To find the angle, we take the inverse sine (arcsin) of 0.8:
θ = arcsin(0.8)
θ ≈ 53° (rounded to the nearest degree)
Therefore, the slide makes an angle of approximately 53 degrees with the ground.