To find out how far from the door the truck should be parked, we need to solve the given equation:
[tex]\[ l = \sqrt{d^2 + h^2} \][/tex]
where:
- \( l \) is the length of the ramp (8 feet),
- \( h \) is the height of the truck bed (2 feet),
- \( d \) is the distance from the door to where the truck should be parked.
We need to find \( d \). Let's follow the steps:
### Step-by-Step Solution
1. Write down the given information:
- Length of the ramp, \( l = 8 \) feet
- Height of the truck bed, \( h = 2 \) feet
- We need to find the distance \( d \)
2. Start with the equation:
[tex]\[ l = \sqrt{d^2 + h^2} \][/tex]
3. Substitute the known values into the equation:
[tex]\[ 8 = \sqrt{d^2 + 2^2} \][/tex]
[tex]\[ 8 = \sqrt{d^2 + 4} \][/tex]
4. Square both sides to remove the square root:
[tex]\[ 8^2 = d^2 + 4 \][/tex]
[tex]\[ 64 = d^2 + 4 \][/tex]
5. Isolate \( d^2 \):
[tex]\[ 64 - 4 = d^2 \][/tex]
[tex]\[ 60 = d^2 \][/tex]
6. Solve for \( d \):
[tex]\[ d = \sqrt{60} \][/tex]
7. Simplify or approximate the square root:
[tex]\[ d \approx 7.745966692414834 \][/tex]
Therefore, the truck should be parked approximately 7.75 feet from the door for an eight-foot ramp to reach a truck bed that is two feet above the ground.
