find the lenth of cable needed for cable car to reach top of mountain from a point up the mountain

Question

A steep mountain is inclined 78 degrees from the horizontal and rises 3000 vertical feet above the surrounding plain. A cable car is to be installed that will travel from a point 860 ft from the base of the mountain to the top. Find the shortest length of cable needed.

draw a diogram and solve.

Your answer is   __________ ft;

Answer 1

Are you sure the cable car isn't travelling from a point 860 ft from the base, along the ground? As in the following diagram:

If this is the case, you can use ³⁰⁰⁰/_x = tan(78°) to find x, and then the Pythagorean Theorem to find y