The length of the lift line represents the hypotenuse of a right triangle. The side opposite the given angle is the height of the mountain. The applicable trig relation is ...
Sin = Opposite/Hypotenuse
We want to find the hypotenuse, so we use the rearranged form ...
hypotenuse = (mountain height)/sin(33°)
lift length = (544 m)/sin(33°) ≈ 998.83 m
The length of the lift from bottom to top is about 999 meters.
