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 inclined at 15 degree to the horizontal.
Answer to the nearest metre.
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.