A steep mountain is inclined 74 degree to the horizontal and

A steep mountain is inclined 74 degree to the horizontal and rises h = 3600 ft above the surrounding plain. A cable car is to be installed from a point d = 850 ft from the base to the top of the mountain, as shown. Find the shortest length of cable needed. (Round your answer to the nearest foot.) ft

Solution

shortest length = sqrt(h² + (d+ (h/tan74))²)

= sqrt(3600² + (850 + (3600/tan74))²)

= sqrt(12960000 + 3542990.755)

= 4062.387322 ft