Solve the Problem $L$ Of a Highway Sag Curve Can Be Computed By

Solve the problem.
-The minimum length $L$ of a highway sag curve can be computed by
$$\mathrm { L } = \frac { \left( \theta _ { 2 } - \theta _ { 1 } \right) \mathrm { S } ^ { 2 } } { 200 ( \mathrm {~h} + \mathrm { S } \tan \alpha ) ^ { \prime } }$$
where $\theta _ { 1 }$ is the downhill grade in degrees $\left( \theta _ { 1 } < 0 ^ { \circ } \right) , \theta _ { 2 }$ is the uphill grade in degrees $\left( \theta _ { 2 } > 0 ^ { \circ } \right) , \mathrm { S }$ is the safe stopping distance for a given speed limit, $h$ is the height of the headlights, and $\alpha$ is the alignment of the headlights in degrees. Compute $L$ for a 55 -mph speed limit, where $h = 1.6 \mathrm { ft }$ , $\alpha = 0.8 ^ { \circ } , \theta _ { 1 } = - 5 ^ { \circ } , \theta _ { 2 } = 1 ^ { \circ }$ , and $S = 336 \mathrm { ft }$ . Round your answer to the nearest foot.

A) $525 \mathrm { ft }$
B) $553 \mathrm { ft }$
C) $568 \mathrm { ft }$
D) $538 \mathrm { ft }$