In a national park, the distance between the base of two cliffs is 312 feet. The angle of elevation from the bae of the shorter cliff to the top of the taller cliff is 35 degrees. The angle of elevation from the base of the taller cliff to the top of the shorter cliff is 27 degrees. The tops of the two cliffs are joined by a bridge of length x, as modeled below.

Using trig ratios, the height of the shorter cliff is

The height of the taller cliff is

The difference between the heights of the two cliffs is

The length of the bridge is