Question

A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 840 ft out in the plain from the base of the mountain. Find the shortest length of cable needed. Round your answer to the nearest foot.

Answer 1

Answer:

3854ft

Step-by-step explanation:

By assuming that the cable is not doubled.

in order to find the length of the base of the mountain

tan74°=3400/x

x= 3400/tan74°

x≈ 975ft

Therefore, the length of the cable equals to

            =$\sqrt{3400^2+(975 + 840)^2}$

length≈ 3854ft

Thus, the shortest length of cable needed is 3854ft