The ski lift is 560m long, how long is the top of the ski lift vertically from the foot of the mountain?A ski lift is travelling up a mountain is...

We  consider the ski lift to be in a vertical plane and
the corresponding geometrical figure is as below:

Let us
draw a right angled triangle ABC representing the data.

AB
makes an angle of 15 degree with BC .

Let AB = 560 m
representing the ski lift which is inclined at an angle of 15 degree to the horizontal
plane.

BC is a a horizontal line from the bottom of the ski
lift.

Angle B= 15 degree.

A is
the top point of the ski lift.

C is the foot of
perpendicular from A on horizontal line BC.

Now ABC is a
right angled triangle.

Therefore, by definition, sineB =
opposite side / hypotenuse

Therefore, sin B =
AC/AB

Therefore  AC =
AB*sinB

Therefore AC = (560 m )sine15 = 144.9387
m nearly.

Therefore the heit of the ski lift = AC =
144.9387 m , or 145 m.