Question
- 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?
ground level.
a) If the exit ramp is to rise at an angle of
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
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
b) Horizontal distance needed: 29.85 m
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg


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:
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
.