Question

a steep mountain is inclined 80 degrees from the horizontal and rises 3400 vertical feet above the surrounding plain. a cable car is to be installed that will travel from a point 990 ft from the base of the mountain to the top. find the shortest length of cable needed.

Answer 1

3753.20 ft

Explanation:

tan 80° = 3400 ft/x

x = 599.51 ft = distance at ground level from point directly below mountain peek to edge of mountain.

599.51 ft + 990 ft = 1589.51 ft = horizontal distance at ground level from where cable is attached to the ground to the center of the mountain. This is a leg of a right triangle.

3400 ft is another leg of a right triangle.

(1589.51 ft)² + (3400 ft)² = y²

The hypotenuse, y, is the length of the cable.

y = 3753.20 ft