Pregunta
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The angle of inclination from the base of skyscraper A to the top of skyscraper is approximately . If skyscraper
B is 1451 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are ai the same
elevation.
The distance from skyscraper A to skyscraper B is feet.
(Round to two decimal places as needed.)

Ask by Carroll Park. in the United States
Jan 30,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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The distance between the two skyscrapers is approximately 1,394.37 feet.

Solución

To find the distance between the two skyscrapers, we can use the tangent function from trigonometry.
Given:
  • Angle of inclination from the base of skyscraper A to the top of skyscraper B:
  • Height of skyscraper B: 1451 feet
We can use the tangent function to find the distance between the two skyscrapers. The tangent function is defined as:
In this case, the opposite side is the height of skyscraper B (1451 feet), and the adjacent side is the distance between the two skyscrapers (which we want to find).
Let’s denote the distance between the two skyscrapers as .
Using the tangent function, we have:
Now, we can solve for by rearranging the equation:
Let’s calculate the value of using the tangent function.
The distance between the two skyscrapers is approximately 1394.37 feet.
Therefore, the distance between the two skyscrapers is 1394.37 feet.

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Extra Insights

To find the distance between the two skyscrapers, we can use trigonometric functions. In this case, we can apply the Law of Sines in the triangle formed by the two skyscrapers and the line of sight.
Since the angle of inclination from the base of skyscraper A to the top of skyscraper B is , the angle at the base (formed by the horizontal line from A to B) is:
Next, we know the height of skyscraper B is 1451 feet. We can then use the tangent function:
So, simplifying we have:
Thus, the distance between the two skyscrapers is approximately feet.
To round to two decimal places, the final answer is:
The distance from skyscraper A to skyscraper B is feet.

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