Kendra walked diagonally across a rectangular field that is 45 m by 65 m. To the nearest degree, at what angle, adjacent to the longer side, did she walk? 

To find the angle at which Kendra walked diagonally across the rectangular field, we can use trigonometry. Specifically, we'll use the tangent function, which is defined as:

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

In this context:
- The opposite side is the shorter side of the rectangle, which is \(45\) meters.
- The adjacent side is the longer side of the rectangle, which is \(65\) meters.
- \(\theta\) is the angle adjacent to the longer side.

So we have:

\[
\tan(\theta) = \frac{45}{65}
\]

Now, calculate \(\theta\) by taking the arctangent (inverse tangent) of the ratio:

\[
\theta = \tan^{-1}\left(\frac{45}{65}\right)
\]

\[
\theta = \tan^{-1}\left(0.6923\right)
\]

Using a calculator to find the angle:

\[
\theta \approx 34.99^\circ
\]

To the nearest degree, Kendra walked at an angle of **35°** adjacent to the longer side of the field.

Would you like further details or have any questions?

### Related Questions:
1. What is the length of the diagonal that Kendra walked across?
2. How would the angle change if the field was 50 m by 70 m?
3. What is the sine of the angle Kendra walked at?
4. How can you use the Pythagorean theorem to find the diagonal length of the field?
5. What if Kendra walked across the shorter side instead? What would be the angle then?
6. Can this angle be used to determine the aspect ratio of the field?
7. What is the cosine of the angle she walked at?
8. How would the angle change if Kendra started walking from the corner adjacent to the shorter side?

**Tip:** The tangent function is useful for calculating angles when you know the lengths of the two sides of a right triangle, particularly in real-world applications like navigation and surveying.

Learn how to calculate the angle adjacent to the longer side that Kendra walked at in a rectangular field measuring 45 m by 65 m using trigonometry. To the nearest degree, find the angle using the tangent function. Suitable for high school students learning trigonometry.

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