https://file.aiquickdraw.com/mathbot/file/1728750560715nb3t7gc2.jpg

Let's go through the tasks in the image:

### Aufgabe 1: Berechne die Länge der Seite \( x \)
This problem involves solving for side \( x \) in various triangles using trigonometry, likely applying the sine or cosine rules since the angles and other sides are given.

- (a) Given a triangle with sides 5.2 cm, angle 37°, and side 2.7 cm. Use the Law of Sines.
- (b) Similar approach, involving Law of Sines or Cosines.
- (c) Requires solving for side \( x \) using angles 47°, 32°, and the adjacent side of 17.5 m.
- (d) Involves an angle of 57°, opposite side of 11.3 cm.

### Aufgabe 2: Berechne den Winkel \( \alpha \)
This problem asks for the calculation of angle \( \alpha \) in various triangles:

- (a) A triangle with sides 9.1 cm, 6.9 cm, and 5.8 m.
- (b) Similar triangle, with sides given.
- (c) Requires determining \( \alpha \) given sides of 4.4 m and 2.9 m.
- (d) A larger triangle, using side lengths 23.6 dm and 12.7 dm.

### Aufgabe 3: Bestimme die Steigungen der folgenden Schanzen in Prozent
For this task, we compute the slopes of ski jumps:

- a) Calculate the slope for various jumps with the angles provided.
- b) The Letalnica-Schanze (Slovenia) problem asks to compute height using a given run-up length of 116.5 m. This involves using trigonometric functions.

### Aufgabe 4: Berechne die fehlenden Größen auf zwei verschiedene Arten
Solve for the missing dimensions of triangles using different methods, likely applying trigonometric identities or rules:

- Each sub-problem (a)-(d) involves finding sides and angles, using tools like the Pythagorean theorem or trigonometric ratios.

### Aufgabe 5: Bestimme die Steigungswinkel der folgenden „Pisten“
This problem asks to compute the steepness of slopes (like ski slopes or bike climbs):

- The slopes are given in percentages, requiring the use of tangent function to convert the percentage into a slope angle.

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Would you like me to solve a specific problem from this list, or would you like an example calculation for one of the tasks? 

Here are some questions that build on these tasks:
1. How do you use the Law of Sines to calculate unknown sides in non-right triangles?
2. What is the difference between using sine and cosine rules in trigonometry?
3. How do you convert slope percentages into angles using the tangent function?
4. What is the best way to check if a triangle solution is correct when using trigonometry?
5. How do you interpret the given angles and slopes in real-world applications like ski jumps?

**Tip**: Always double-check the angle measures and sides when working with non-right triangles, as small errors in these can lead to large discrepancies in results.

The original page contains various trigonometry tasks, including calculations of side lengths, angles, slopes, and real-world applications of triangles.

Solve trigonometry problems involving the calculation of side lengths, angles, and slopes. The tasks cover real-world applications such as ski jumps and slopes, using key concepts like the Law of Sines, Cosines, and trigonometric functions. Suitable for students in Grades 10-12.

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