Question
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  1. An underground parking lot is being constructed 8.00 m below
    ground level.
    a) If the exit ramp is to rise at an angle of , how long will the
    ramp be? Round your answer to the nearest hundredth of a metre
    b) What horizontal distance, to the nearest hundredth of a metre, is
    needed for the ramp?

Ask by Wood Tucker. in Canada
Dec 16,2024

Upstudy AI Solution

Tutor-Verified Answer

Answer

a) Length of the ramp: 30.90 m
b) Horizontal distance needed: 29.85 m

Solution

To solve the problem, we can use some basic trigonometry.

Part a: Length of the Ramp

We know that the ramp rises at an angle of and the vertical height it needs to cover is . We can use the sine function, which relates the opposite side (the height) to the hypotenuse (the length of the ramp).
The formula is:
Where:
  • (length of the ramp)
Rearranging the formula gives us:
Calculating :
Now substituting this value into the equation:
So, the length of the ramp is approximately 30.90 m.

Part b: Horizontal Distance Needed for the Ramp

To find the horizontal distance, we can use the cosine function, which relates the adjacent side (the horizontal distance) to the hypotenuse (the length of the ramp).
The formula is:
Where:
  • (horizontal distance)
  • (length of the ramp)
Rearranging the formula gives us:
Calculating :
Now substituting this value into the equation:
So, the horizontal distance needed for the ramp is approximately 29.85 m.

Summary of Answers:

a) Length of the ramp: 30.90 m
b) Horizontal distance needed: 29.85 m

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Beyond the Answer

To find the length of the ramp, we can use the sine function. Since the ramp makes an angle of with the horizontal, we can set up the equation as follows:
where L is the length of the ramp. Rearranging gives , which calculates to approximately .
For the horizontal distance, we can use the cosine function. The formula is , where is the horizontal distance. Substituting the ramp length calculated, gives a horizontal distance of about .

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