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You are going to use an incline plane to lift a heavy object to the top of a shelving unit with a height of 7 ft. The base of the incline plane is 10 ft from the shelving unit. What is the length of the incline plane?
The length of the incline plane is about ___ ft.
(Round to the nearest tenth as needed.)
To find the length of the incline plane, we can use the Pythagorean theorem. The incline plane, the height of the shelving unit, and the base form a right triangle.
1. Identify the values:
– Height (opposite side) = 7 ft
– Base (adjacent side) = 10 ft
2. Apply the Pythagorean theorem:
[
c^2 = a^2 + b^2
]
where ( c ) is the length of the incline plane (hypotenuse), ( a ) is the height, and ( b ) is the base.
3. Plug in the values:
[
c^2 = 7^2 + 10^2
]
[
c^2 = 49 + 100
]
[
c^2 = 149
]
4. Calculate ( c ):
[
c = sqrt{149} approx 12.2 text{ ft}
]
So, the length of the incline plane is about 12.2 ft (rounded to the nearest tenth).