# 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 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.

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### 1 Answer

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.