Answer:
3917m
Step-by-step explanation:
We are given that
[tex]\theta=74^{\circ}[/tex]
[tex]h=3400 ft[/tex]
We have to find the shortest length of cable needed.
Let Base=x
We know that
[tex]tan\theta=\frac{Perpendicular\;side}{Base}[/tex]
Using the formula
[tex]tan74^{\circ}=\frac{3400}{x}[/tex]
[tex]x=\frac{3400}{tan74}=975m[/tex]
[tex]y=x+970=975+970=1945m[/tex]
Now, the length of cable needed
=[tex]\sqrt{(3400)^2+(1945)^2}[/tex]
=3917m
Hence, the shortest length of cable needed=3917m