A​ one-lane highway runs through a tunnel in the shape of​ one-half a sine curve cycle. The opening is 36 feet wide at road level and is 19 feet tall at its highest point. ​(a) Find an equation for the sine curve that fits the opening. Place the origin at the left end of the opening. ​(b) If the road is 18 feet wide with 9​-foot shoulders on each​ side, what is the height of the tunnel at the edge of the​ road?