Answer:
B. 4557 ft
Step-by-step explanation:
In this problem we have to types of triangles. We have a right triangle and a not right triangle.
The side we have to find is part of the not right triangle, so there we would have to use the law of cosines. However, that triangle isn't complete. So, we first have to find the hypothenuse of the right triangle AC, and then apply the law of cosines for the upper triangle.
We have to apply trigonometric reasons to find the hypothenuse, because we know only one side and one angle of the right triangle. So,
[tex]sin28\°=\frac{1800}{AC}\\\\ AC=\frac{1800}{sin28\°}=3834ft[/tex]
Now we have AC, we apply the law of cosines to the upper triangle ACD
[tex]CD^{2}=AC^{2}+AD^{2}-2AC.AD.cos34\°\\ CD=\sqrt{(3834)^{2}+(7200)^{2}-2(3834)(7200)(cos34\°)}\\CD=4557ft[/tex]
Therefore, the right answer is B. 4557 ft.
