Question

A steep mountain is inclined 72 degree to the horizontal and rises 4500 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 900 ft from the base of the mountain. Find the shortest length of cable needed.

Answer 1

`l_c=5078.27ft`

Step-by-step explanation:

From the question we are told that:

Angle of inclination
`\angle=72 \textdegree`

Height
`h=4500ft`

Distance b\w cable base and mountain base
`d_(cm)=900ft`

Generally the equation for length of mountain base
`d_(mb)` is mathematically given by

`Tan\theta=(h)/(d_(mb))`

`d_(mb)=(h)/(Tan\theta)`

`d_(mb)=(4500)/(Tan 72 \textdegree)`

`d_(mb)=1462.11ft`

Generally the Pythagoras equation for length of the cable
`l_c` is mathematically given by

`l_c^2=h^2+(d_(mb)+d_(cm)^2)`

`l_c^2=4500^2+(1462.11}+900}^2)`

`l_c=5078.27ft`