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zzz [600]
2 years ago
11

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.
Mathematics
1 answer:
elena55 [62]2 years ago
7 0

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

Diana is 17.6 feet closer to the building

<h3>How to calculate the distance from the building</h3>

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

\tan(\theta) = \frac{h}{d}

Where:

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

So, we have:

\tan(40) = \frac{130}{d}

Make d the subject

d = \frac{130}{\tan(40)}

Evaluate tan(40)

d = \frac{130}{0.8391}

d = 154.93

Initially, Diana is at a distance of 172.53.

The difference in both distance is:

\Delta d = 172.53 - 154.93

\Delta d = 17.6

Hence, Diana is 17.6 feet closer to the building

Read more about trigonometry ratios at:

brainly.com/question/4326804

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