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Para 1-15, se proporciona información sobre los lados y/o ángulos del triángulo rectángulo Resuelve completamente el triángulo (encuentra todos los lados y ángulos que faltan) con 1 decimal.ABC

The table in the image contains information related to solving right triangles, specifically focusing on sides and angles for different problem numbers (labeled 1 to 5). The goal is to solve each triangle by finding all missing sides and angles to one decimal place.

I'll extract and solve each triangle using the given data. Let's go through them one by one.

### Problem 1:
Given:
- Angle \( A = 90^\circ \)
- Angle \( C = 6^\circ \)
- Side \( c = 7 \) (assumed to be the hypotenuse because \( A = 90^\circ \))

1. Angle \( B \):
   \[
   B = 90^\circ - C = 90^\circ - 6^\circ = 84^\circ
   \]

2. Side \( a \) (opposite angle \( A \)):
   \[
   a = c \cdot \sin(C) = 7 \cdot \sin(6^\circ) \approx 7 \cdot 0.1045 \approx 0.7
   \]

3. Side \( b \) (adjacent to angle \( C \)):
   \[
   b = c \cdot \cos(C) = 7 \cdot \cos(6^\circ) \approx 7 \cdot 0.9945 \approx 7.0
   \]

### Problem 2:
Given:
- Angle \( A = 90^\circ \)
- Side \( a = 7 \)
- Side \( c = 11 \) (assumed to be the hypotenuse)

1. Angle \( C \):
   \[
   \sin(C) = \frac{a}{c} = \frac{7}{11} \approx 0.6364
   \]
   \[
   C \approx \sin^{-1}(0.6364) \approx 39.5^\circ
   \]

2. Angle \( B \):
   \[
   B = 90^\circ - C \approx 90^\circ - 39.5^\circ = 50.5^\circ
   \]

3. Side \( b \):
   \[
   b = c \cdot \cos(C) \approx 11 \cdot \cos(39.5^\circ) \approx 11 \cdot 0.777 \approx 8.5
   \]

### Problem 3:
Given:
- Angle \( A = 90^\circ \)
- Angle \( B = 37^\circ \)
- Side \( b = 22 \)

1. Angle \( C \):
   \[
   C = 90^\circ - B = 90^\circ - 37^\circ = 53^\circ
   \]

2. Side \( c \) (hypotenuse):
   \[
   c = \frac{b}{\cos(B)} = \frac{22}{\cos(37^\circ)} \approx \frac{22}{0.7986} \approx 27.5
   \]

3. Side \( a \) (opposite angle \( C \)):
   \[
   a = b \cdot \tan(C) = 22 \cdot \tan(53^\circ) \approx 22 \cdot 1.327 \approx 29.2
   \]

### Problem 4:
Given:
- Angle \( A = 90^\circ \)
- Side \( b = 6 \)
- Angle \( C = 11^\circ \)

1. Angle \( B \):
   \[
   B = 90^\circ - C = 90^\circ - 11^\circ = 79^\circ
   \]

2. Side \( c \) (hypotenuse):
   \[
   c = \frac{b}{\cos(C)} = \frac{6}{\cos(11^\circ)} \approx \frac{6}{0.9816} \approx 6.1
   \]

3. Side \( a \):
   \[
   a = c \cdot \sin(C) \approx 6.1 \cdot \sin(11^\circ) \approx 6.1 \cdot 0.1908 \approx 1.2
   \]

### Problem 5:
Given:
- Angle \( A = 90^\circ \)
- Angle \( C = 10^\circ \)
- Side \( c = 17 \) (hypotenuse)

1. Angle \( B \):
   \[
   B = 90^\circ - C = 90^\circ - 10^\circ = 80^\circ
   \]

2. Side \( a \) (opposite angle \( C \)):
   \[
   a = c \cdot \sin(C) = 17 \cdot \sin(10^\circ) \approx 17 \cdot 0.1736 \approx 3.0
   \]

3. Side \( b \):
   \[
   b = c \cdot \cos(C) = 17 \cdot \cos(10^\circ) \approx 17 \cdot 0.9848 \approx 16.7
   \]

Would you like a detailed explanation of any specific problem, or do you have any questions?

Here are five related questions:
1. How do you determine which side is the hypotenuse in a right triangle?
2. Why do we subtract one angle from 90° to find the other non-right angle?
3. How does the sine function relate to the sides of a right triangle?
4. What is the significance of knowing the hypotenuse when solving a right triangle?
5. How can you use the cosine function to find an unknown side of a right triangle?

**Tip:** Always check if your calculated angles add up to 180° to confirm the accuracy of your solutions for triangles.

Explore how to solve right triangles by finding all missing sides and angles to one decimal place. This detailed explanation covers the use of the Pythagorean theorem, sine, cosine, and tangent functions. Suitable for high school students studying trigonometry.

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