Answer
The height of the triangular sail is $16$ feet.
Work Step by Step
We know that the area of a triangle can be given by the formula:
$$A = \frac{1}{2}bh$$
In this problem, we know that the base $b$ is $15$ feet long. We also know that the area of this triangular sail is $120$ square feet. We can plug these two values into the formula for the area of a triangle:
$$120 = \frac{1}{2}(15)h$$
Let's simplify by multiplication:
$$120 = \frac{15}{2}h$$
Divide both sides by $\frac{15}{2}$, which means multiply both sides by the reciprocal, which is $\frac{2}{15}$:
$$120(\frac{2}{15}) = h$$
Solve for $h$ by multiplying:
$$h = 16$$
The height of the triangular sail is $16$ feet.
