Question

The angle of elevation from the bottom of the ski lift too the top of the mountain is 62. if the vertical height mountain is 1760 feet what is the total distance traveled on the ski lift from the bottom to the top of the mountain?

A) 1952.8 ft
B) 1993.3 ft
C) 2020.5 ft
D) 2084.1 ft
E) 2102.7 ft

Answer 1

Answer: 1993.3 ft

Let’s visualize this as a right triangle (figure attached).

In a right triangle we can use trigonometric functions, in this case we need to find the the total distance traveled on the ski lift from the bottom to the top of the mountain, which is represented by the hypotenuse
`h` of this triangle, while the vertical height of the mountain is the Opposite side
`OS` to the elevation angle
`\theta=62\º`.

The trigonometric function that best fits in this case is sine:

`sin\theta=(OS)/(h)` (1)

Finding
`h` and substituting the known values:

`h=(OS)/(sin\theta)` (2)

`h=(1760ft)/(sin(62\º))` (3)

We finally find the total distance traveled on the ski lift from the bottom to the top of the mountain:

`h=1993.32 ft`

Hence, the correct option is B.