Answer:
[tex]l_c=5078.27ft[/tex]
Step-by-step explanation:
From the question we are told that:
Angle of inclination [tex]\angle=72 \textdegree[/tex]
Height [tex]h=4500ft[/tex]
Distance b\w cable base and mountain base [tex]d_{cm}=900ft[/tex]
Generally the equation for length of mountain base [tex]d_{mb}[/tex] is mathematically given by
[tex]Tan\theta=\frac{h}{d_{mb}}[/tex]
[tex]d_{mb}=\frac{h}{Tan\theta}[/tex]
[tex]d_{mb}=\frac{4500}{Tan 72 \textdegree}[/tex]
[tex]d_{mb}=1462.11ft[/tex]
Generally the Pythagoras equation for length of the cable [tex]l_c[/tex] is mathematically given by
[tex]l_c^2=h^2+(d_{mb}+d_{cm}^2)[/tex]
[tex]l_c^2=4500^2+(1462.11}+900}^2)[/tex]
[tex]l_c=5078.27ft[/tex]
