https://file.aiquickdraw.com/mathbot/file/1725964050602mg2qjh9t.jpg

To solve the problem:

We are given:
- The height of the vertical stick, \( h = 8 \, \text{m} \)
- The length of the shadow, \( s = 6 \, \text{m} \)

The angle of elevation of the sun, \( \theta \), can be found using trigonometry, specifically by applying the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{s}
\]
Substituting the values:
\[
\tan(\theta) = \frac{8}{6} = \frac{4}{3}
\]
To find \( \theta \), we take the arctangent (inverse tangent) of \( \frac{4}{3} \):
\[
\theta = \tan^{-1}\left( \frac{4}{3} \right)
\]

Let me calculate the angle.It seems like I can’t do more advanced data analysis right now. Please try again later.

In the meantime, you can use a scientific calculator or calculator app to find the inverse tangent of \( \frac{4}{3} \) (which is approximately 1.3333). This will give you the angle of elevation in degrees.

Would you like to explore more details, or have any other questions? Here are some related questions to consider:

1. How can you use the sine or cosine functions to solve similar problems?
2. How would the angle of elevation change if the shadow length increased?
3. Can you derive the height of the object if the angle and shadow length are given?
4. What are real-world applications of finding angles of elevation?
5. How would you solve this problem if the given units were different (e.g., feet instead of meters)?

**Tip:** The tangent function is particularly useful when working with right triangles involving heights and shadow lengths!

A vertical stick is 8 m high and the length of its shadow is 6 m. What is the angle of elevation of the sun?

Solve a trigonometry problem involving a vertical stick of 8 m and a shadow of 6 m. Learn how to calculate the angle of elevation of the sun using tangent and arctangent functions. This solution explains the use of trigonometric ratios and is suitable for Grades 8-10.

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