Problem #$2$: Horizontal curves $(10$ points$)$

A back tangent has a bearing of $N53{42}^{\text{'}}{20}^{\text{'}\text{'}}E$ meets a forward tangent with a bearing of $S38{30}^{\text{'}}{00}^{\text{'}\text{'}}E$ at PI STA $24+50\mathrm{.}00.$ A horizontal curve with radius $=875\mathrm{.}00$ feet will be used to connect the two tangents. Compute the tangent distance, length of curve, as well as stations at the beginning of the curve and the end of the curve.