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

`\frac{\sin8^\circ}{7600\,\mathrm{ft}}=(\sin16^\circ)/(BC)\implies BC=\frac{(7600\,\mathrm{ft})\sin16^\circ}{\sin156^\circ}\approx15052\,\mathrm{ft}`

b. In triangle BCD, we have

`\sin24^\circ=(CD)/(BC)`

and so

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