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)?
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(1 point)
The distance from the back of the truck to the edge of the ramp is about
inches.
194 is not the correct answer
To find the longest distance that the ramp can be extended, we need to find the length of the hypotenuse of a right triangle formed by the ramp and the ground. The height of the moving van can be considered as the perpendicular side of the triangle, and the length of the ramp can be considered as the base of the triangle.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
hypotenuse^2 = height^2 + base^2
hypotenuse^2 = 32^2 + 196^2
hypotenuse^2 = 1024 + 38416
hypotenuse^2 = 39440
Taking the square root of both sides, we find:
hypotenuse = √39440
hypotenuse ≈ 198.58
Rounded to the nearest whole number, the distance from the back of the truck to the edge of the ramp is 199 inches.
To find the longest distance that the ramp can be extended, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length of the ramp is the hypotenuse, and we need to find the length of the base, which is the distance from the back of the truck to the edge of the ramp. Let's call that distance x.
Using the Pythagorean theorem, we have:
x^2 + 32^2 = 196^2
x^2 + 1024 = 38416
x^2 = 37492
Taking the square root of both sides, we get:
x ≈ 193.63
Therefore, the longest distance that the ramp can be extended (rounded to the nearest whole number) is approximately 194 inches.
To find the longest distance that the ramp can be extended, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the distance from the back of the truck to the edge of the ramp forms the hypotenuse of a right triangle, the height of the moving van forms one side, and the length of the ramp forms the other side.
Let's call the unknown distance from the back of the truck to the edge of the ramp x.
Using the Pythagorean theorem, we have:
x^2 = 196^2 + 32^2 (since the length of the hypotenuse is x, the height is 32, and the length of the ramp is 196)
Simplifying this equation:
x^2 = 38416 + 1024
x^2 = 39440
Taking the square root of both sides:
x ≈ 198.58
Therefore, the longest distance that the ramp can be extended is approximately 198.58 inches.
Rounding to the nearest whole number, the distance is about 199 inches.