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This image contains two main sections of problems involving right triangles and trigonometry. Let's work through them step by step.

### 1. **Resolver los siguientes triángulos rectangulos**
   In this section, we need to solve for missing sides and angles of the given right triangles using trigonometric ratios (sine, cosine, and tangent).

   #### (a) Triangle ABC
   - Angle \( A = 56^\circ 21' 49'' \)
   - Hypotenuse \( AB = 21.09 \)

   To find the other sides, we can use the sine and cosine functions:
   - \( \sin(A) = \frac{opposite}{hypotenuse} = \frac{BC}{AB} \)
   - \( \cos(A) = \frac{adjacent}{hypotenuse} = \frac{AC}{AB} \)

   #### (b) Triangle DEF
   - Angle \( \angle D = 71^\circ \)
   - Side \( DF = 9.34 \)

   Again, use trigonometric ratios:
   - \( \sin(71^\circ) = \frac{EF}{DF} \)
   - \( \cos(71^\circ) = \frac{DE}{DF} \)

   #### (c) Triangle MON
   - Angle \( M = 64^\circ \)
   - Side \( MN = 6.41 \)

   Use:
   - \( \sin(64^\circ) = \frac{ON}{MN} \)
   - \( \cos(64^\circ) = \frac{MO}{MN} \)

   #### (d) Triangle PQR
   - Angle \( \angle Q = 21^\circ 48' \)
   - Hypotenuse \( PQ = 315 \)

   Use:
   - \( \sin(21^\circ 48') = \frac{PR}{PQ} \)
   - \( \cos(21^\circ 48') = \frac{QR}{PQ} \)

---

### 2. **Resolver las siguientes situaciones problemáticas**

   #### (a) Ramp Problem:
   - Length of ramp: \( 2.5 \, \text{m} \)
   - Angle of inclination: \( 27^\circ \)
   - Find the height of the ramp.

   Use:
   \[
   \sin(27^\circ) = \frac{height}{2.5}
   \]

   #### (b) Distance to top of building:
   - Distance from the building: \( 75 \, \text{m} \)
   - Angle of elevation: \( 62^\circ 23' 34'' \)
   - Find the distance to the top of the building.

   Use:
   \[
   \tan(62^\circ 23' 34'') = \frac{height}{75}
   \]

   #### (c) Lighthouse Problem:
   - Height of the lighthouse: \( 55 \, \text{m} \)
   - Angle \( \theta = 21^\circ \)
   - Find the distance from the boat to the base of the lighthouse.

   Use:
   \[
   \tan(21^\circ) = \frac{55}{distance}
   \]

   #### (d) Tree Height Problem:
   - Distance from the tree: \( 9.5 \, \text{m} \)
   - Angle: \( 65^\circ \)
   - Observer’s height: \( 1.81 \, \text{m} \)
   
   To find the total height of the tree:
   \[
   \tan(65^\circ) = \frac{tree\,height - 1.81}{9.5}
   \]

Would you like me to go ahead and calculate all the missing values? Let me know if you'd like more details on any step or specific problem.

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### Related questions:
1. What are the basic trigonometric functions, and how do they relate to right triangles?
2. How do you convert degrees, minutes, and seconds to decimal degrees?
3. What are the common real-life applications of trigonometry, like the problems presented here?
4. How does the angle of elevation affect the distance calculated in a right triangle?
5. What are the differences between solving a right triangle and solving a general triangle?

### Tip:
Always make sure your calculator is set to the correct mode (degrees or radians) based on the angle unit provided in the problem.

The problem involves solving right triangles using trigonometric ratios and calculating distances and heights in real-world scenarios.

This guide explains how to solve right triangles using trigonometric ratios such as sine, cosine, and tangent. Learn how to calculate the height of a ramp, the distance from a boat to a lighthouse, and the height of a tree using real-world trigonometry problems.

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