Answer
$x = 4.6$ ft.
Work Step by Step
The loading ramp is the hypotenuse of this right triangle. The height of the ship's deck above the dock is the side opposite the angle that the ramp makes with the dock. Since we have the measure of one angle and the measure of the hypotenuse, we can use the sine ratio to find $x$, which is the side opposite to the given angle.
The sine ratio is given as follows:
sin $A = \frac{opposite}{hypotenuse}$
Let's plug in what we know:
sin $18^{\circ} = \frac{x}{15}$
Multiply each side by $15$:
sin $18^{\circ}(15) = x$
Multiply to solve for $x$:
$x = 4.6$ ft.
