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.
To find the longest distance that the ramp can be extended, we can use the Pythagorean theorem. The distance from the back of the truck to the edge of the ramp forms a right triangle with the height of the truck and the length of the ramp.
Using the Pythagorean theorem, we have:
(distance from back of truck)^2 + (height of truck)^2 = (length of ramp)^2
Let's plug in the given values:
(distance from back of truck)^2 + 32^2 = 196^2
Simplifying,
(distance from back of truck)^2 + 1024 = 38416
Subtracting 1024 from both sides,
(distance from back of truck)^2 = 37440
Taking the square root of both sides,
distance from back of truck = √37440
Rounded 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 need to find the hypotenuse of a right triangle.
The height of the moving van (the vertical side of the triangle) is 32 inches and the length of the ramp (the horizontal side of the triangle) is 196 inches.
Using the Pythagorean theorem, we can find the hypotenuse:
h^2 = a^2 + b^2
Where h is the hypotenuse, a is the height, and b is the length of the ramp.
Plugging in the values:
h^2 = 32^2 + 196^2
h^2 = 1024 + 38416
h^2 = 39440
To find h, we take the square root of both sides:
h = √39440
h ≈ 198.58
Rounded to the nearest whole number, the longest distance that the ramp can be extended is 199 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 side opposite the right angle) 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 the height of the van and the distance from the back of the truck to the edge of the ramp form the other two sides of the right triangle.
Let's denote the length of the ramp as "x", the height of the van as 32 inches, and the distance from the back of the truck to the edge of the ramp as "y".
According to the Pythagorean theorem, we have:
x^2 = y^2 + 32^2
We also know that the length of the ramp is 196 inches, so we can write:
196^2 = y^2 + 32^2
We can solve this equation to find the value of "y". First, let's calculate the right-hand side of the equation:
y^2 + 32^2 = 1024 + 1024 = 2048
Now, let's substitute this value back into the equation:
196^2 = 2048 + 32^2
Calculating the left-hand side of the equation:
196^2 = 38416
Subtracting 2048 from both sides:
196^2 - 2048 = 38416 - 2048
Simplifying:
-2048 = 36368
To isolate "y^2", we need to add 2048 to both sides of the equation:
y^2 = 36368 + 2048 = 38416
Now, we can find the value of "y" by taking the square root of both sides:
y = sqrt(38416) ≈ 196 inches
So the maximum distance that the ramp can be extended is approximately 196 inches.