$(15$ points$)$ Calculate the elevation at BM$2$ according to the Trigonometric leveling data:

BM$1$ known elevation: $1833\mathrm{.}449$ ft $.$

Slope Distance to BM$1$: $255\mathrm{.}663$ ft $.$

Slope Distance to BM$2$: $277\mathrm{.}733$ ft $.$

Zenith angle to $BM1$:$89{26}^{\text{'}}{36}^{\text{'}\text{'}}$

Zenith angle to BM$2$:$916\text{'}43\text{'}$