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This problem is about solving a right triangle given one angle and one side length. Specifically, you're given:

- Angle \( A = 50^\circ \)
- Side \( a = 22 \) (the side opposite angle \( A \))
- Angle \( B \) is unknown (but it’s a right triangle, so \( C = 90^\circ \))
- Side lengths \( b \) and \( c \) are unknown.

### Step 1: Find Angle \( B \)
Since the sum of the angles in a triangle is always \( 180^\circ \), we can find angle \( B \) using:
\[
B = 90^\circ - A = 90^\circ - 50^\circ = 40^\circ
\]

### Step 2: Find Side \( b \) (adjacent to \( A \))
We can use the tangent function to find \( b \) (the side adjacent to angle \( A \)):
\[
\tan(A) = \frac{a}{b}
\]
\[
b = \frac{a}{\tan(A)} = \frac{22}{\tan(50^\circ)} \approx 18.4
\]

### Step 3: Find Hypotenuse \( c \)
We can use the sine function to find \( c \) (the hypotenuse):
\[
\sin(A) = \frac{a}{c}
\]
\[
c = \frac{a}{\sin(A)} = \frac{22}{\sin(50^\circ)} \approx 28.7
\]

### Final Answers:
- \( B = 40^\circ \)
- \( b \approx 18.4 \)
- \( c \approx 28.7 \)

Would you like more details or clarifications? 

Here are five related questions:
1. How do you solve a right triangle given two sides?
2. What are other ways to find the hypotenuse in a right triangle?
3. How can trigonometric ratios (sine, cosine, tangent) be applied in real-life problems?
4. What is the Pythagorean theorem, and how does it apply to right triangles?
5. How does rounding affect the accuracy of trigonometric calculations?

**Tip:** Always ensure your calculator is in degree mode when working with trigonometric functions involving degrees.

Solve the right triangle with A = 50° and a = 22. Find B, b, and c. Round to the nearest tenth.

Learn how to solve a right triangle given angle A = 50° and side a = 22. Find the other angle and sides using trigonometric ratios. The problem covers key concepts like the sine and tangent functions and the Pythagorean theorem. Suitable for students in Grades 9-11.

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