trig homework help

Question

A steep mountain is inclined 70 degrees from the horizontal and rises 3200 vertical feet above the surrounding plain. A cable car is to be installed that will travel from a point 870 ft from the base of the mountain to the top. Find the shortest length of cable needed. 

Your answer is    ft; 

Answer 1

3405 feet

minimum cable length = square root of (3200^2 + (870+x)^2)= about 3405

where 3200/(870+x) = about 2.75 = tan70

3200/2.75 = 870+x

x = 3200/2.75 -870 = about 294= distance from base of the mountain to the middle of the mountain directly below its highest point of 3200 feet