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At the end of her work day at the Ferguson Corporation, Sarah usually

walks to the subway station to travel home. Today, she is walking to the

Springdale Town Center first to take care of some errands. She will then

continue walking to the subway station to travel home. The map of these

routes is shown below.

2000 feet

Subway

Ferguson

Corporation

Station

Springdale

Town Center

If Sarah walks to the Springdale Town Center from the Ferguson

Corporation and then to the Subway Station, how much farther will she

walk than if she walks directly to the Subway Station from the Ferguson

Corporation? Show all of your work.

Respuesta :

fichoh

Answer:

1263.7032 feets

Step-by-step explanation:

Distance from Ferguson corporation to Springdale Town center ; let the distance = x

Using trigonometry :

Tanθ = opposite / Adjacent

Tan 27 = x / 2000

0.5095254 * 2000 = x

1019.0508 feets

Distance from Springdale to Subway station, this is the hypotenuse :

Hypotenuse = √(1019.0508² + 2000²)

Hypotenuse = √5038464.7

Hypotenuse = 2244.6524 feets

Total distance walked from Ferguson to Springdale, then to Subway ;

(1019.0508 + 2244.6524) feets = 3263.7032 feets

Additional distance walked :

(3263.7032 feets - 2000 feets) = 1263.7032

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lhmarianateixeira

In this exercise we have to calculate the distance knowing about the laws of a triangle, so we have to:

[tex]H=1263.7032 feets[/tex]

We can use the definition of tangent to calculate:

[tex]Tan\theta = opposite / Adjacent\\Tan 27 = X / 2000\\0.5095254 * 2000 = X\\=1019.0508 feets[/tex]

Now using the Pythagorean theorem we have:

[tex]H = \sqrt{(1019.0508^2 + 2000^2)}\\H = \sqrt{5038464.7}\\H = 2244.6524 feets\\(1019.0508 + 2244.6524) = 3263.7032 feets\\(3263.7032 feets - 2000 feets) = 1263.7032[/tex]

See more about triangles at brainly.com/question/2269348

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