https://file.aiquickdraw.com/mathbot/file/1727368698782opjl411i.jpg

The image shows two triangles. I’ll help you with the triangle on the right side, which seems to be the one that involves solving for \( x \).

### Problem Breakdown:

The triangle on the right is a triangle with three labeled angles and sides. Here's a breakdown:
- There is a 58° angle at \( T \), 
- A 39° angle at \( R \),
- A side labeled 28 opposite \( x \).

To find \( x \), you can use the **Law of Sines**, which states:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
Where:
- \( A \), \( B \), and \( C \) are the angles of the triangle,
- \( a \), \( b \), and \( c \) are the sides opposite to these angles.

#### Steps to Solve:
1. Calculate the third angle in the triangle \( \triangle TSR \), which can be found by using the fact that the sum of the interior angles of a triangle is 180°. 

\[
\angle S = 180^\circ - 58^\circ - 39^\circ = 83^\circ
\]

2. Now, apply the Law of Sines:

\[
\frac{x}{\sin(58^\circ)} = \frac{28}{\sin(83^\circ)}
\]

3. Solve for \( x \):

\[
x = \frac{28 \times \sin(58^\circ)}{\sin(83^\circ)}
\]

Let me calculate that for you.The value of \( x \) is approximately 23.92.

Would you like further details or clarifications on this process?

Here are five related questions to explore:

1. How is the Law of Sines applied to non-right triangles?
2. Can the Law of Cosines be used for this triangle? If so, how?
3. What happens when two sides and an angle are known in a triangle?
4. How can the Law of Sines help in real-world applications?
5. What is the difference between solving for angles and sides using trigonometry?

**Tip**: Always ensure that the angles in a triangle add up to 180° when using the Law of Sines or solving triangles in general!

Solve for x in a triangle with angles 58°, 39°, and a side opposite x of length 28.

Use the Law of Sines to solve for the unknown side x in a triangle with angles 58°, 39°, and a side opposite the unknown angle of length 28. A step-by-step guide using the Law of Sines for students in Grades 9-12.

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