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Homework:9.1 HW - Applications Involving Right Triangles
Question 22, 9.1.41
HW Score: 88%, 22 of 25 points
 Points: 0 of 1


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Part 1
The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately 12.9degrees. If skyscraper B is 1426 feet​ tall, how far apart are the two​ skyscrapers? Assume the bases of the two buildings are at the same elevation.
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Part 1
The distance from skyscraper A to skyscraper B is about 
  
enter your response here feet.
​(Round to the nearest integer as​ needed.)
The distance from skyscraper A to skyscraper B is about(Round to the nearest integer as needed.)
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To solve this problem, we can apply the trigonometric functions related to right triangles. The situation involves a right triangle where:

- The height of skyscraper B is the opposite side to the angle of inclination.
- The distance between the two skyscrapers is the adjacent side.
- The angle of inclination is given as 12.9°.

We can use the tangent function because tangent relates the opposite side and the adjacent side in a right triangle:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case:
- \(\theta = 12.9^\circ\),
- opposite = 1426 feet (the height of skyscraper B),
- adjacent = the unknown distance between the skyscrapers.

Rearranging the formula to solve for the adjacent side (the distance between the skyscrapers):

\[
\text{adjacent} = \frac{\text{opposite}}{\tan(\theta)}
\]

Substitute the values:

\[
\text{adjacent} = \frac{1426}{\tan(12.9^\circ)}
\]

Now calculate the tangent of 12.9° and then divide 1426 by it:

\[
\text{adjacent} = \frac{1426}{\tan(12.9^\circ)} \approx \frac{1426}{0.228}
\]

\[
\text{adjacent} \approx 6257 \text{ feet}.
\]

Thus, the distance between the two skyscrapers is approximately 6257 feet.

If you need more details or have any questions, feel free to ask!

Here are 5 related questions you could explore:
1. How would the calculation change if the angle of inclination was 15° instead of 12.9°?
2. What is the height of skyscraper A if the angle of inclination to the top of skyscraper B is reduced by half?
3. How does the tangent function help in solving right triangle problems involving distances?
4. What if the two skyscrapers were at different elevations? How would that affect the calculation?
5. Can you derive a similar equation using the sine or cosine function for other types of problems?

**Tip**: Always ensure that your calculator is set to degrees, not radians, when solving angle-related problems.

The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately 12.9 degrees. If skyscraper B is 1426 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation.

Learn how to find the distance between two skyscrapers using trigonometry. Given the angle of inclination of 12.9° and a height of 1426 feet for one of the skyscrapers, this problem applies the tangent function in right triangles to find the solution. Suitable for students in Grades 9-12.

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