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Let's break down the problem from the image you uploaded:

The task is to calculate the height \( h \) of the inaccessible cliff (Steilwandstück) based on the given information:

- \( e = 6 \) meters (the horizontal distance from point \( A \) to point \( B \)).
- Two angles are provided:
  - \( \alpha = 24^\circ \) (angle at point \( A \)),
  - \( \beta = 38^\circ \) (angle at point \( B \)).

### Steps to Solve

We can approach this problem using trigonometry. Since we have a right triangle (triangle \( ABD \)), we can use the **law of sines** or apply trigonometric identities directly.

#### Step 1: Calculate angle \( \gamma \) at point \( D \)
Since the sum of angles in a triangle is \( 180^\circ \), and triangle \( ABD \) is a right triangle, we can determine the third angle \( \gamma \):
\[
\gamma = 180^\circ - \alpha - \beta = 180^\circ - 24^\circ - 38^\circ = 118^\circ.
\]

#### Step 2: Use trigonometry to find height \( h \)
Now, we can apply the tangent function, because tangent relates the opposite side (height \( h \)) to the adjacent side (base \( e \)):

For angle \( \beta \):
\[
\tan(\beta) = \frac{h}{e}.
\]

Solving for \( h \):
\[
h = e \cdot \tan(\beta) = 6 \cdot \tan(38^\circ).
\]

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

However, you can easily compute the height \( h \) by following these steps:

1. Use the formula:
   \[
   h = 6 \times \tan(38^\circ).
   \]
2. Calculate the tangent of \( 38^\circ \) using a calculator, then multiply by 6 to get \( h \).

If you'd like more assistance or have questions, feel free to ask!

Here are five related questions for further practice:

1. How would you calculate the height if the angle \( \beta \) was changed to 45 degrees?
2. What would happen if the distance \( e \) increased to 10 meters?
3. How can you calculate the length of the side \( CD \) directly?
4. How does the sine function relate to this problem?
5. What would be the effect of decreasing angle \( \alpha \) on the height \( h \)?

**Tip:** When dealing with right triangles, always think about the relationship between the sides and angles using trigonometric functions like sine, cosine, and tangent.

Berechnen Sie die Höhe h des unzugänglichen Steilwandstücks in Metern! Gegeben: Entfernung e = 6 Meter, Winkel α = 24° und β = 38°.

Learn how to calculate the height of an inaccessible cliff using trigonometry. Given the horizontal distance (6 meters) and angles (24° and 38°), we solve for the height using the tangent function. This problem demonstrates the use of key trigonometric identities and is suitable for high school students in Grades 10-12.

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