A ramp is 10 feet in length. The ramp is lifted 4 feet off the ground to the truck door. What is the distance across the ground from the bottom of the ramp to the ground underneath the truck door? Approximate to the nearest hundredth. ≈ 3.46 feet ≈ 5.29 feet ≈ 9.17 feet ≈ 10.77 feet

Accepted Solution

Answer:The distance is 9.17 feet.Step-by-step explanation:The ramp, vertical distance it is lifted, and the ground form a right triangle, whose hypotenuse the ramp, and whose base and perpendicular are the ground and the lifted distance respectively.Thus we have a triangle whose hypotenuse [tex]H[/tex] is 10 feet, the perpendicular [tex]P[/tex] is 4 feet, and a base [tex]B[/tex] feet. The Pythagorean theorem gives:[tex]H^2=P^2+B^2[/tex]We substitute the values [tex]H=10[/tex], [tex]P =4[/tex] and solve for B:[tex]B=\sqrt{H^2-P^2} =\sqrt{10^2-4^2} =9.17.[/tex]Thus the distance is 9.17 feet.