Question

If you could please show all your steps that would be great.

Answer 1

a. Angles ABC and CBD are supplementary, so you know that $m\angle ABC=180^\circ-24^\circ=156^\circ$

The interior angles of any triangle sum to 180 degrees in measure, so that $m\angle ACB=180^\circ-156^\circ-16^\circ=8^\circ$.

By the law of sines, we then have

$\dfrac{\sin8^\circ}{7600\,\mathrm{ft}}=\dfrac{\sin16^\circ}{BC}\implies BC=\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}$

b. In triangle BCD, we have

$\sin24^\circ=\dfrac{CD}{BC}$

and so

$CD=\sin24^\circ\dfrac{(7600\,\mathrm{ft})\sin16^\circ}{\sin8^\circ}\approx6122\,\mathrm{ft}$