Answer: The guy wire = 393.4 ft
Step-by-step explanation:
Given images:
Refer to the attachment below (I apologize for the bad writing on the computer)
Given information:
Height of the tower = 175 ft
Height of the wire = 15 ft from the top (Opposite)
Angle with the ground = 24°
Length of wire = Unknown (Hypotenuse)
Determine the trigonometric function:
The primary choice will be the Sine function because the angle is opposite to the height and the wire is the hypotenuse of the system.
Determine the equation:
sin θ = (Opposite) / (Hypotenuse)
sin (24°) = (175 - 15) / (Length)
Simplify value in parenthesis
sin (24°) = (160) / (Length)
Multiply the Length of wire on both sides
sin (24°) * (Length) = (160) / (Length) * (Length)
sin (24°) * (Length) = (160)
Divide sin (24°) on both sides
sin (24°) * (Length) / sin (24°) = (160) / sin (24°)
Length = 160 / sin (24°)
[tex]\Large\boxed{Length~=~393.4~ft}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
