A truck approaching a tunnel of semi-circular(cross section) with a maximum height of 5.25m. If the load is 8m wide and 3.5m high, will it fit into the tunnel?
The maximum clearance for the truck would be if it drove straight down the center line of the tunnel.
In order for the truck to fit, the corners of the load must fit within the perimeter of the tunnel. In order to determine if this will happen we need to realize that the diagonal which runs from the center of the road directly below the center of the truck up through the upper most corner of the load must be less than the radius of the tunnel.
The diagonal in question represents the hypotenuse of a right triangle which has a base half the width of the truck's load, and an altitude equal to the truck's load. Therefore the diagonal of the truck will be
`D =sqrt(x^2 + y^2) = sqrt(4^2 + 3.5^2)` m
`D = sqrt(16 + 12.25) = sqrt(28.25) = 5.32 m`
5.32 m > 5.25m maximum radius, so No, the truck will not fit.