For a right triangle with legs $a$ and $b$, the area is $\frac12 ab$. Substitute $a=15$ and area $=120$ to find the missing leg.

At angle $x$ (at the end of the boom), $\tan x=\frac{\text{opposite leg}}{\text{adjacent leg}}$.

Enter 2*120/15 to compute the mast height $h$.

Divide the height by the boom length by entering (2*120/15)/15, then match the exact value to the choices.

Because the boom and mast are perpendicular, they are the legs of the right triangle. If the mast height is $h$, then

Solve $\frac12(15)h=120$:

Angle $x$ is at the end of the boom, so the adjacent leg is the boom ($15$) and the opposite leg is the mast height ($16$). Thus,

Therefore, the correct choice is $\frac{16}{15}$.