Solve the Problem $\mathrm { L }$ Of a Highway Sag Curve Can Be Computed By

Multiple Choice

Solve the problem.
-The minimum length $\mathrm { L }$ of a highway sag curve can be computed by
$$\mathrm { L } = \frac { \left( \theta _ { 2 } - \theta _ { 1 } \right) \mathrm { S } ^ { 2 } } { 200 ( \mathrm {~h} + \mathrm { S } \tan \alpha ) }$$
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 $h = 1.9 \mathrm { ft }$ , $\alpha = 0.7 ^ { \circ } , \theta _ { 1 } = - 5 ^ { \circ } , \theta _ { 2 } = 4 ^ { \circ }$ , and $S = 336 \mathrm { ft }$ . Round your answer to the nearest foot.

A) $824 \mathrm { ft }$
B) $893 \mathrm { ft }$
C) $846 \mathrm { ft }$
D) $869 \mathrm { ft }$