Answer:
The length of the wire is 76.19 m.
Step-by-step explanation:
It is given that a guy wire is attached to the top of a radio antenna and to a point on horizontal ground that 40 m from the base of the antenna.
It means base of the right angled triangle is 40 m.
The wire makes an angle of 58deg 20min with the ground.
1 degree = 60 min
Using this conversion convert the given angle in degree.
[tex]58^{\circ}20'=58^{\circ}\frac{20}{60}^{\circ}=58\frac{1}{3}^{\circ}=\frac{175}{3}^{\circ}[/tex]
In a right angled triangle
[tex]\cos \theta=\frac{adjacent}{hypotenuse}[/tex]
[tex]\cos (\frac{175}{3}^{\circ})=\frac{40}{hypotenuse}[/tex]
[tex]0.525=\frac{40}{hypotenuse}[/tex]
[tex]hypotenuse=\frac{40}{0.525}[/tex]
[tex]hypotenuse=76.190[/tex]
Therefore the length of the wire is 76.19 m.
