The length of each guy wire can be calculated using trigonometry. By applying the cosine function to the adjacent side (32 feet) and the angle (71 degrees), we can determine the formula:
Length of guy wire = Adjacent / cos(Angle)
Substituting the given values:
Length of guy wire = 32 / cos(71 degrees)
Calculating the cosine of 71 degrees to be approximately 0.307:
Length of guy wire = 32 / 0.307
Which simplifies to:
Length of guy wire ≈ 104.228
Therefore, rounded to the nearest tenth, each guy wire needs to be approximately 104.2 feet in length.
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To find the length of each guy wire, we can use trigonometry. We'll use the cosine function because we have the adjacent side (32 feet) and the angle (71 degrees). The formula is:
Length of guy wire
=
Adjacent
cos
(
Angle
)
Length of guy wire=
cos(Angle)
Adjacent
Substituting the values:
Length of guy wire
=
32
cos
(
7
1
∘
)
Length of guy wire=
cos(71
∘
)
32
Now, we need to calculate the cosine of 71 degrees:
cos
(
7
1
∘
)
≈
0.307
cos(71
∘
)≈0.307
Length of guy wire
=
32
0.307
Length of guy wire=
0.307
32
Length of guy wire
≈
104.228
Length of guy wire≈104.228
Rounded to the nearest tenth, each guy wire needs to be approximately 104.2 feet long.
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