A support wire to a tower is anchored 45 feet from the base of the tower at a 68.5° angle to the ground. What can you say about the angle between the ground and the support wire if... A support wire to a tower is anchored 45 feet from the base of the tower at a 68.5° angle to the ground. What can you say about the angle between the ground and the support wire if the wire starts farther away from the tower?
Understand the Problem
The question is asking about the relationship between the angle of a support wire to a tower and the distance from the base of the tower when the distance increases. We need to determine how the angle changes as the wire moves farther away from the tower.
Answer
The angle would increase.
Answer for screen readers
The angle would increase.
Steps to Solve
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Understanding the setup The support wire forms a triangle with the ground and the tower. The 45 feet from the base of the tower is the horizontal leg of a right triangle.
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Identifying the angle The given angle of $68.5^{\circ}$ is the angle between the ground and the wire.
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Analyzing the effect of distance As the wire moves farther away from the tower, the distance from the base (horizontal leg) increases. This affects the angle:
- If we visualize this scenario, as the distance increases while keeping the height of the tower constant, the angle between the wire and the ground must open up.
- Determining the relationship When the horizontal distance increases, the triangle becomes wider. Therefore, the angle between the ground and the wire increases.
The angle would increase.
More Information
As the horizontal distance from the tower increases, the angle formed between the wire and the ground gets larger, leading to a more acute angle relative to the ground.
Tips
- Confusing the relationship between the angle and the distance. Many might assume the angle stays the same, but it actually increases due to the nature of right triangles.
