We can solve this question using the next drawing to better see the situation:
Then, to find the distance AB, we can use the Law of Cosines, as follows:
[tex]c^2=a^2+b^2-2a\cdot b\cdot\cos (C)[/tex]Then, we have that:
c = d = ?
a = 860 ft
b = 175 ft
cos(C) = cos(78)
Thus, applying the formula, we can substitute each of the value on it, as follows:
[tex]c^2=860^2+175^2-2\cdot(860)\cdot(175)\cdot\cos (78)[/tex]Then, we have:
[tex]c^2=739600+30625-301000\cdot\cos (78)[/tex][tex]c^2=707643.581064ft^2[/tex]Thus
[tex]\sqrt[]{c^2}=\sqrt[]{707643.581064ft^2}\Rightarrow c=841.215538ft[/tex]Therefore, the distance from A to B (rounded to the nearest hundredth) is c = 841.22 ft.
