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. Click Here for Help Video.
(1 point)
The distance from the back of the truck to the edge of the ramp is about
inches.
the correct answer is not 194, or 199
To find the longest distance that the ramp can be extended, we need to use the Pythagorean theorem. The length of the ramp is the hypotenuse of a right triangle, and the height of the van is one of the legs.
The length of the ramp is 196 inches.
The height of the van is 32 inches.
Let's call the longest distance from the back of the truck to the edge of the ramp x.
Using the Pythagorean theorem, we can write the equation:
x^2 = 196^2 - 32^2
x^2 = 38416 - 1024
x^2 = 37492
Taking the square root of both sides, we get:
x ≈ 193.66
Rounding to the nearest whole number, the longest distance that the ramp can be extended is about 194 inches.
To find the longest distance that the ramp can be extended, we need to calculate the hypotenuse of the right triangle formed by the ramp, the ground, and the height of the moving van.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
Where c is the hypotenuse, and a and b are the other two sides of the triangle.
In this case, one side is the height of the moving van (b = 32 inches), and the other side is the distance from the truck to the edge of the ramp (a).
Rearranging the formula, we can solve for a:
a = sqrt(c^2 - b^2)
Plugging in the given measurements:
c = 196 inches
b = 32 inches
a = sqrt((196)^2 - (32)^2)
a = sqrt(38416 - 1024)
a = sqrt(37492)
a ≈ 193.6 inches
Rounding the answer to the nearest whole number, the distance from the back of the truck to the edge of the ramp is approximately 194 inches.
To find the longest distance that the ramp can be extended, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we can treat the distance from the back of the truck to the edge of the ramp as the hypotenuse, and the height of the moving van to the ground as one of the other sides. Using the given measurements:
Height of the van = 32 inches
Length of the ramp = 196 inches
Let's call the distance from the back of the truck to the edge of the ramp "x". We can write the equation:
x^2 = 196^2 + 32^2
x^2 = 38416 + 1024
x^2 = 39440
To find x, we take the square root of both sides:
x = √39440
x ≈ 198.6 inches
Rounding to the nearest whole number, the longest distance that the ramp can be extended is approximately 199 inches.