a ramp 10ft long is connected to the back of a truck that is 4ft off the ground. how far away from the truck does the ramp touch the ground?
since it forms a triangle, use pythagorean theorem:
c^2 = a^2 + b^2
where c = 10, a = 4 (the height) and b is the unknown (the base),,
therefore:
10^2 = 4^2 + b^2
84 = b^2
b = 2*sqrt(21) = 9.165 ft
so there,, :)
To find out how far away from the truck the ramp touches the ground, we can use the concept of similar triangles.
Let's consider two right triangles here:
1. Triangle formed by the truck, the ground, and the point where the ramp touches the ground.
2. Triangle formed by the truck, the ramp, and the point where the ramp touches the ground.
Since these two triangles are similar, we can set up a proportion to find the length of the ramp where it touches the ground.
In the first triangle, the height (or distance from the truck to the ground) is 4ft. In the second triangle, the distance from the truck to the ramp (which we need to find) can be represented as 𝑥.
The proportion we can set up is:
𝑥/10ft = 4ft/0ft
Cross-multiplying, we get:
𝑥 = (4ft × 10ft) / 0ft
Since anything divided by 0 is undefined, this equation cannot be solved. Therefore, the ramp does not touch the ground if it is connected 4ft off the ground on the back of a truck.