Question
A telephone tower casts a 50-foot shadow that makes a 48° angle with the ground. If Fiona wants to find the length of the cable that secures the tower to the ground, how should she set up the problem?
Option #1: cos48°=x50
cos
48
°
=
𝑥
50
Option #2: cos48°=50x
cos
48
°
=
50
𝑥
Option #3: cos50°=50x
cos
50
°
=
50
𝑥
(1 point)
Option # is the correct setup.
Option #1: cos48°=x50
cos
48
°
=
𝑥
50
Option #2: cos48°=50x
cos
48
°
=
50
𝑥
Option #3: cos50°=50x
cos
50
°
=
50
𝑥
(1 point)
Option # is the correct setup.
Answers
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Answered by
GPT-4o mini
To find the length of the cable that secures the tower to the ground, we can use trigonometry. The angle given (48°) is between the ground and the line of the cable. The shadow (50 feet) represents the adjacent side of a right triangle, while the length of the cable (hypotenuse) is what we want to find.
Using the cosine function, which relates the angle to the adjacent side and hypotenuse, the setup is:
\[
\cos(48°) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{50}{x}
\]
Where:
- \( \cos(48°) \) is the cosine of the angle,
- 50 is the length of the shadow (adjacent),
- \( x \) is the length of the cable (hypotenuse).
Rearranging gives us:
\[
x = \frac{50}{\cos(48°)}
\]
Thus, the correct option is:
**Option #1: \( \cos 48° = \frac{x}{50} \)**
Using the cosine function, which relates the angle to the adjacent side and hypotenuse, the setup is:
\[
\cos(48°) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{50}{x}
\]
Where:
- \( \cos(48°) \) is the cosine of the angle,
- 50 is the length of the shadow (adjacent),
- \( x \) is the length of the cable (hypotenuse).
Rearranging gives us:
\[
x = \frac{50}{\cos(48°)}
\]
Thus, the correct option is:
**Option #1: \( \cos 48° = \frac{x}{50} \)**
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