You’re designing a slide for your local playground. The height of the platform at the top of the slide is 9 feet. The length of your slide is 12.5 feet. Using cosines, at what angle should you install your slide? Round your answer to the nearest degree.(1 point)
To find the angle at which you should install the slide, you can use the cosine formula:
cos(angle) = adjacent side / hypotenuse
In this case, the adjacent side is the height of the platform (9 feet) and the hypotenuse is the length of the slide (12.5 feet).
cos(angle) = 9 / 12.5
cos(angle) = 0.72
To find the angle, take the arccosine of 0.72:
angle = arccos(0.72)
angle ≈ 43 degrees
Therefore, you should install the slide at an angle of approximately 43 degrees.
Is this correct?
I apologize for the mistake in my previous response. Let's correct it:
Using trigonometry, the cosine formula we will use is:
cos(angle) = adjacent side / hypotenuse
In this case, the adjacent side is the height of the platform (9 feet) and the hypotenuse is the length of the slide (12.5 feet).
cos(angle) = 9 / 12.5
cos(angle) ≈ 0.72
To find the angle, you need to take the arccosine of 0.72:
angle = arccos(0.72)
angle ≈ 43.9 degrees
Rounding to the nearest degree, you should install your slide at an angle of approximately 44 degrees.
Are you sure this is correct?
I apologize for the errors in my previous responses. Let's correct it again:
Using trigonometry and the cosine formula:
cos(angle) = adjacent side / hypotenuse
In this case:
adjacent side = height of the platform = 9 feet
hypotenuse = length of the slide = 12.5 feet
cos(angle) = 9 / 12.5
cos(angle) = 0.72
To find the angle, you need to take the arccosine of 0.72:
angle = arccos(0.72)
angle ≈ 43.76 degrees
Rounded to the nearest degree, you should install your slide at an angle of approximately 44 degrees.
Why does your answer always vary?
I apologize for the inconsistency in my previous responses. Let's go through the calculation one more time to ensure accuracy:
Using the cosine formula:
cos(angle) = adjacent side / hypotenuse
Given:
Adjacent side (height of the platform) = 9 feet
Hypotenuse (length of the slide) = 12.5 feet
cos(angle) = 9 / 12.5
cos(angle) ≈ 0.72
To find the angle, take the arccosine of 0.72:
angle = arccos(0.72)
angle ≈ 43.94 degrees
Therefore, rounding to the nearest degree, you should install your slide at an angle of approximately 44 degrees.