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: $4004.76\ ft$

Step-by-step 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

$\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft$