https://r2.erweima.ai/mathbot/image/1726416602083ja6a6h1z.pdf

The uploaded document appears to be an academic improvement plan (plan de mejoramiento académico) for 10th-grade mathematics students from the "Institución Educativa Rodrigo Lara Bonilla." The document includes instructions for students to recover pending grades by solving exercises on trigonometry. Here's a summary of the tasks:

### Key tasks:
1. **Trigonometric Ratios**: Students are required to calculate the six trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) for given right triangles.
   
2. **Word Problems Involving Elevation and Depression Angles**:
   - **a)** A kite flown with a 300-meter string at a 60° angle with the ground. Find the height of the kite.
   - **b)** A skier descends a hill of 108 meters at a 30° depression angle. Calculate the distance covered by the skier.
   - **c)** A boat views a lighthouse at a 20° elevation angle. If the lighthouse is 24 meters tall, find the distance of the boat from the lighthouse.
   - **d)** A building casts a shadow of 950 meters with the sun's rays at a 25° elevation angle. Find the building's height.
   - **e)** A plane is flying at 10,000 meters with a 30° elevation angle from an observer. Determine the distance from the observer to the plane.
   - **f)** A ramp is 400 meters long and rises vertically by 32 meters. Find the angle of elevation.

3. **Law of Sines**: Solve the triangles using the Law of Sines.

The document also mentions presentation guidelines and grading criteria for recovery work.

Would you like detailed solutions for any of these problems or assistance on a specific concept?

### Relative Questions:
1. How are the six trigonometric ratios calculated for right triangles?
2. What is the relationship between angles of elevation and depression in solving word problems?
3. How can the Law of Sines be applied to non-right triangles?
4. What is the role of the angle of elevation in determining height or distance in real-world problems?
5. How do trigonometric ratios help in understanding right triangles geometrically?

**Tip**: When solving for unknowns in trigonometric problems, ensure your calculator is set to the correct unit (degrees or radians) based on the given angle.

How to solve various trigonometric problems involving right triangles, elevation and depression angles, and the Law of Sines?

Learn how to solve right triangle problems using trigonometric ratios, and apply the Law of Sines for non-right triangles. This guide covers practical problems, such as calculating the height of a kite or the distance from a boat to a lighthouse. Perfect for 10th-grade math students.

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