If we look at the picture, we have a right triangle, where we want to find the measure of an angle and we know the value of the two legs.
The trigonometric relationship that involves an angle, and the two legs is tangent
For an angle x:
[tex]\tan x=\frac{\text{opposite leg}}{adjacent\text{ leg}}[/tex]In this case, the leg opposite to angle x is the one of length 110ft, and the adjacent to angle x is the one of length 90ft.
Then we write:
[tex]\tan x=\frac{110ft}{90ft}[/tex]And solve for x:
[tex]\begin{gathered} \tan x=\frac{11}{9} \\ x=\arctan (\frac{11}{9}) \\ x=50.71º \end{gathered}[/tex]Thus, the correct answer is option b.