Question

A steep mountain is inclined 75 degree to the horizontal and rises 3900 ft above the surrounding plain. A cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 910 ft from the base of the mountain. Find the shortest length of cable needed.

Answer 1

Answer:
`4004.76\ ft`

Explanation:

Given

inclination is
`\theta=75^(\circ)`

Mountain is
`h=3900\ ft` high

Cable is tied
`x=910\ ft` from the base of the mountain

From the figure, length of the shortest path is
`l`

It is given by using Pythagoras theorem

`\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=√((3900)^2+(910)^2)\\\Rightarrow l=4004.76\ ft`