https://file.aiquickdraw.com/mathbot/file/1729733871192sdmatqbw.jpg

Let's analyze the question and the triangle in the provided image.

This is a **right triangle** with a given side of 8 ft and an angle of \(30^\circ\). To determine which equation solves for \(b\), we need to choose the appropriate trigonometric ratio.

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**Step-by-step approach:**

1. **Identify the given values:**
   - The side of 8 ft is opposite the 30° angle (side \(BC\)).
   - \(b\) is the hypotenuse (\(b = AB\)).
   - \(c\) is the adjacent side to the angle (but irrelevant to our question).

2. **Determine which trigonometric function relates the hypotenuse and the opposite side:**
   - **Sine** function relates the opposite side and hypotenuse:  
     \[
     \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
     \]

3. **Set up the equation:**
   \[
   \sin(30^\circ) = \frac{8}{b}
   \]

4. **Solve for \(b\):**
   \[
   b = \frac{8}{\sin(30^\circ)}
   \]

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**Correct answer:**
The correct option is:
\[
b = \frac{8}{\sin(30^\circ)}
\]

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Would you like further details on how trigonometric functions work or how to use them in other cases?

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### 5 Related Questions:
1. What are the values of sine, cosine, and tangent for other standard angles like 45° and 60°?
2. How do you solve for an adjacent side using cosine instead of sine?
3. What are the conditions for using tangent in a right triangle?
4. How does the sine function behave for angles larger than 90°?
5. Can you derive the value of \(\sin(30^\circ)\) from an equilateral triangle?

**Tip:** Memorizing the standard trigonometric values for angles like 30°, 45°, and 60° helps solve such problems quickly.

Which equation can be used to solve for b?

Learn how to solve for the hypotenuse 'b' in a right triangle with a given angle of 30°. This problem uses trigonometric ratios, specifically the sine function, to find the unknown side. Suitable for students in Grades 9-10.

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