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.