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Explanation:
See the attached image below. The information that the tower is 500 ft is never used. Focus solely on triangle ABD (ignore point C).
AB = 200
AD = x = unknown
angle ABD = angle B = 47 degrees
Use the cosine rule to help find x
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cos(angle) = adjacent/hypotenuse
cos(B) = AB/BD
cos(47) = 200/x
x*cos(47) = 200
x = 200/cos(47)
x = 293.255837127926
Rounding to the nearest foot, we get 293 feet as the answer.
The length of the guy wire is 273.5 feet.
Trigonometric ratio show the relationship between the sides and angles of a right angled triangle.
Let d represent the length of the guy wire.
Using trigonometric ratios:
[tex]sin(47)=\frac{200}{d} \\\\d=\frac{200}{sin(47)} \\\\d=273.5\ feet[/tex]
The length of the guy wire is 273.5 feet.
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