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.