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5. On a college campus, the library is 80 yards due east of the dormitory and the recreation center is due north of the
library. The college is constructing a sidewalk from the dormitory to the recreation center. The sidewalk will be at a
56° angle with the current sidewalk between the dormitory and the library. To the nearest yard, how long will the new
sidewalk be?

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ajeigbeibraheem

The length of the new sidewalk between the Dormitory to the recreation center is 143 yards

We need to understand the concept of Bearing and Distance in order to be able to determine how long is the new sidewalk.

What are Bearing and Distance?

The Bearing of an angle measures the movement of an angle in a clockwise direction starting from the North Pole. However, the distance shows how the length of the sides of the angle can also be measured.

From the diagram attached below:

  • The adjacent of the sidewalk way = 80 yards.
  • The hypotenuse shows the new sidewalk way  = x( unknown)
  • The angle θ = 56°

Using the relation from trigonometry:

[tex]\mathbf{Cos \ \theta = \dfrac{adjacent}{hypotenuse}}[/tex]

[tex]\mathbf{Cos \ 56 = \dfrac{80 \ yards }{x}}[/tex]

[tex]\mathbf{x= \dfrac{80 \ yards }{Cos \ 56 }}[/tex]

[tex]\mathbf{x= 143.06 \ yards}[/tex]

x ≅ 143 yards

Learn more about Bearing and distance here:

https://brainly.com/question/17007896

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