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A string running from the ground to the top of a fence has an angle of elevation of 45°. The string is 10 feet long. What is the distance between the fence and where the string is pegged to the ground?

Respuesta :

Answer: The distance between the fence and where the string is pegged to the ground is 7.07 feet.

Step-by-step explanation:

Since we have given that

Length of string = 10 feet

Angle of elevation = 45°

We need to find the distance between the fence and where the string is pegged to the ground.

We will apply "Cosine formula "

[tex]\cos 45^\circ=\dfrac{Base}{Hypotenuse}\\\\\dfrac{1}{\sqrt{2}}=\dfrac{Base}{10}\\\\Base=\dfrac{10}{\sqrt{2}}\\\\Base=7.07\ feet[/tex]

Hence, the distance between the fence and where the string is pegged to the ground is 7.07 feet.

Ver imagen windyyork
akposevictor

Applying trigonometry ratio, the distance from where the string is pegged to the ground and the fence is approximately: 7.1 ft.

Recall:

  • Trigonometry ratios can be used to find missing lengths and angles of a right-angled triangle.
  • It is denoted as: SOH CAH TOA

The information given has be sketched out in the diagram attached below.

Thus:

  • Angle of elevation [tex](\theta) = 45^{\circ}[/tex]
  • Hypotenuse = 10 ft
  • Adjacent = distance between the fence and where the string is pegged = x

To find x, apply CAH, which is:

[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

  • Plug in the values

[tex]cos(45) = \frac{x}{10}\\\\[/tex]

  • Multiply both sides by 10

[tex]10 \times cos(45) = x\\\\\mathbf{x = 7.07 }[/tex]

Therefore, applying trigonometry ratio, the distance from where the string is pegged to the ground and the fence is approximately: 7.1 ft.

Learn more here:

https://brainly.com/question/11831029

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