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If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot. 10. 3 ft 17. 6 ft 30. 2 ft 97. 2 ft.

Respuesta :

MrRoyal

The closer Diana gets to the building, the smaller the angle becomes

Diana is 17.6 feet closer to the building

How to calculate the distance from the building

To calculate the distance between her and the building, we make use of the following tangent ratio

[tex]\tan(\theta) = \frac{h}{d}[/tex]

Where:

  • [tex]\theta = 40^o[/tex]
  • h represents the height of the building; h = 130
  • d represents the distance from the building

So, we have:

[tex]\tan(40) = \frac{130}{d}[/tex]

Make d the subject

[tex]d = \frac{130}{\tan(40)}[/tex]

Evaluate tan(40)

[tex]d = \frac{130}{0.8391}[/tex]

[tex]d = 154.93[/tex]

Initially, Diana is at a distance of 172.53.

The difference in both distance is:

[tex]\Delta d = 172.53 - 154.93[/tex]

[tex]\Delta d = 17.6[/tex]

Hence, Diana is 17.6 feet closer to the building

Read more about trigonometry ratios at:

https://brainly.com/question/4326804

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