Problema Solution
A ski-lift that runs to the top of a hill has a rise to run ratio of 3/7. The horizontal distance from the bottom of the lift to the center of the mountain is 3000 ft. How high is the hill? If necessary, round your answer to the nearest tenth of a foot and label it ft..
Answer provided by our tutors
3/7 = rise to run ratio.
That is, in a right triangle, the height by the hyportenuse = 3/7
Hence, angle of elevation of the mountain = sin-1 3/7
Now, the base of the triangle is given as 3000ft
so, height / base = tan (sin-1 3/7)
=> height = base * tan(sin-1 3/7)
=> height = 1423.024 = 1423.0 (rounded)