To determine the maximum height a passing truck can be to fit through the tunnel, we need to use the concept of similar triangles.
The semi-ellipse shape of the tunnel can be represented as an isosceles triangle and a semicircle joined together. The width of the tunnel at the base is given as 36 feet. This means the width of each half of the ellipse (isosceles triangle) is 36/2 = 18 feet.
Let's assume the height of the passing truck is "h" feet.
Since the truck is 12 feet wide, it should fit within the width of the tunnel, which is 18 feet across the base. Therefore, we can set up a proportion:
12 ft / 18 ft = h ft / r ft
Where "r" represents the radius of the semicircle, and "h" represents the height of the truck.
For the proportion, the radius of the semicircle is half the width of the tunnel, so r = 18/2 = 9 feet. Substituting these values into the proportion, we have:
12 ft / 18 ft = h ft / 9 ft
To find h, we can cross-multiply and solve for h:
12 ft * 9 ft = 18 ft * h ft
108 ft^2 = 18 ft * h ft
Divide both sides by 18 ft:
6 ft = h ft
Therefore, the maximum height of the passing truck should be 6 feet to fit through the tunnel.