[tex]\text{total length=}572.62\text{ m}[/tex]
Explanation
Step 1
a) the wire at 65 ° ( red)
we have a rigth triangle (B) so
let
length of the wire= hypotenuse
angle=65 °
opposite side= 100
hence, we need use a funciton that relates those three values
[tex]\sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}}[/tex]
replace
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \sin 65=\frac{100}{\text{wire}1} \\ \text{wire}1=\frac{100}{\sin 65} \\ \text{wire}1=110.33 \end{gathered}[/tex]
Step 2
now, let's find the distnace x
[tex]\begin{gathered} \cos \theta=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \text{hyp}\cdot\cos \theta=x \\ \text{replace} \\ 110.33\cdot\cos 65=x \\ 46.63=x \end{gathered}[/tex]
Step 3
now, find wire 2
[tex]\begin{gathered} \text{wire}2\cdot\cos 50=x \\ \text{wire}2=\frac{x}{\cos 50} \\ \text{wire}2=\frac{46.63}{\cos 50} \\ \text{wire}2=72.54 \end{gathered}[/tex]
Step 4
finally, to find the total length of the wire
, add
total length= (wire1+wire2+4+4)*3times
replace
[tex]\begin{gathered} \text{total length= (110.33+72.54+8)}\cdot3 \\ \text{total length=}572.62\text{ m} \end{gathered}[/tex]
therefore, the answer is
[tex]\text{total length=}572.62\text{ m}[/tex]
I hope this helps you
