An incline ramp on a moving van measures 196 inches. The height of the moving van to the ground is 32 inches. What is the longest distance that the ramp can be extended (the distance from back of the truck to the edge of the ramp when the ramp is at rest on the ground)?
Round your answer to the nearest whole number.
Let's call the longest distance that the ramp can be extended $x$.
If we draw a right triangle with the incline ramp representing the hypotenuse, the height of the moving van representing one of the legs, and $x$ representing the other leg, we can use the Pythagorean theorem to find $x$.
The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, we have:
$x^2 + 32^2 = 196^2$
$x^2 + 1024 = 38416$
$x^2 = 38416 - 1024$
$x^2 = 37492$
Taking the square root of both sides, we find:
$x = \sqrt{37492} \approx 193.6$
Rounding to the nearest whole number, the longest distance that the ramp can be extended is 194 inches.
To find the longest distance that the ramp can be extended, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the van (32 inches) is one side of the right triangle, and the length of the ramp (196 inches) is the hypotenuse. Let's call the third side x.
Using the Pythagorean theorem, we have:
x^2 = 196^2 - 32^2
Simplifying the right side of the equation:
x^2 = 38416 - 1024
x^2 = 37392
Taking the square root of both sides to solve for x:
x = √37392
x ≈ 193.38
Therefore, the longest distance that the ramp can be extended (rounded to the nearest whole number) is approximately 193 inches.
To find the longest distance that the ramp can be extended, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the moving van forms one of the sides, and the horizontal distance from the back of the truck to the edge of the ramp forms the other side. The length of the ramp forms the hypotenuse.
Let's denote the horizontal distance as x, and the length of the ramp as L.
We have the following information:
Height of the moving van (opposite side) = 32 inches
Length of the ramp (hypotenuse) = L
Horizontal distance (adjacent side) = x
According to the Pythagorean theorem, we have:
L^2 = x^2 + 32^2
To find the longest distance that the ramp can be extended, we need to solve for x.
x^2 = L^2 - 32^2
Since we want to find the maximum value of x, we need to find the maximum value of L^2.
To do this, we need to consider the given information that the incline ramp on the moving van measures 196 inches. This means that the length of the ramp itself is 196 inches.
Substituting this into our equation, we have:
x^2 = 196^2 - 32^2
Simplifying,
x^2 = 38416 - 1024
x^2 = 37392
Taking the square root of both sides,
x = sqrt(37392)
x ≈ 193.37
Therefore, the longest distance that the ramp can be extended (the distance from the back of the truck to the edge of the ramp when the ramp is at rest on the ground) is approximately 193 inches. Rounded to the nearest whole number, this is 193 inches.