a. Angles ABC and CBD are supplementary, so you know that [tex]m\angle ABC=180^\circ-24^\circ=156^\circ[/tex]
The interior angles of any triangle sum to 180 degrees in measure, so that [tex]m\angle ACB=180^\circ-156^\circ-16^\circ=8^\circ[/tex].
By the law of sines, we then have
[tex]\dfrac{\sin8^\circ}{7600\,\mathrm{ft}}=\dfrac{\sin16^\circ}{BC}\implies BC=\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}[/tex]
b. In triangle BCD, we have
[tex]\sin24^\circ=\dfrac{CD}{BC}[/tex]
and so
[tex]CD=\sin24^\circ\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin8^\circ}\approx6122\,\mathrm{ft}[/tex]
