A single-lane street 10 ft. wide goes through a semicircular tunnel with radius 9 ft. How high is the tunnel at the edge of each lane? Round off to 2 decimal places.

Answer 1

The semicircle with a radius of 9ft has a height of 9ft (or x² + y² = 9²) and a distance. Also, from center-to-edge is 5 ft for a total of 10 feet from left to right (or 5² + y² = 9² ). Therefore, the maximum rectangle that fits within the semicircle is y = √(81 - 25), 7.48 feet.

Answer 2

x² + y² = 81; x = 5ft, then y = (81 - 25)^1/2 = 56^1/2 = 7.48 ft