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.

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 $b$: $b = \frac{8}{\sin(30^\circ)}$

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

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

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.