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. the distance from the back of the truck to the edge of the ramp is about?
To find the longest distance that the ramp can be extended, we can use the Pythagorean theorem.
The height of the moving van to the ground is the vertical leg of the right triangle, measuring 32 inches. The length of the ramp is the hypotenuse, measuring 196 inches. Let's call the distance from the back of the truck to the edge of the ramp "x".
Using the Pythagorean theorem, we have:
x^2 + 32^2 = 196^2
Simplifying the equation:
x^2 + 1024 = 38416
Subtracting 1024 from both sides:
x^2 = 37442
Taking the square root of both sides:
x ≈ 193.42
Rounding to the nearest whole number, the distance from the back of the truck to the edge of the ramp is about 193 inches.
To find the longest distance 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 is equal to the sum of the squares of the other two sides.
In this case, the height of the moving van to the ground is one side of the right triangle, and the length of the ramp is the other side. The longest distance that the ramp can be extended is the hypotenuse of the right triangle.
Using the Pythagorean theorem, we can calculate the length of the ramp. Let's denote the length of the ramp as "x".
According to the Pythagorean theorem:
x² = (height of the van)² + (length of the ramp)²
x² = 32² + 196²
x² = 1024 + 38416
x² = 39440
Taking the square root of both sides:
x = √39440
x ≈ 198.596
Rounding to the nearest whole number, the longest distance that the ramp can be extended is approximately 199 inches. Therefore, the distance from the back of the truck to the edge of the ramp when the ramp is at rest on the ground is about 199 inches.
To find the distance from the back of the truck to the edge of the ramp when the ramp is at rest on the ground, we'll use the Pythagorean theorem. The Pythagorean theorem 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, we have a right triangle with the height of the moving van (32 inches) as one side and the length of the incline ramp (196 inches) as the hypotenuse. We want to find the length of the other side, which is the distance from the back of the truck to the edge of the ramp.
Let's call this distance "x". We can set up the equation as follows:
x^2 + 32^2 = 196^2
Simplifying the equation:
x^2 + 1024 = 38416
x^2 = 38416 - 1024
x^2 = 37492
Taking the square root of both sides:
x = sqrt(37492)
Using a calculator, we find:
x ≈ 193.63 inches
Rounding this to the nearest whole number, 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 194 inches.