The given equation to solve for the length of line segment $AC$ is:

$\sin(40^\circ) = \frac{b}{20}$

Where:

• $b = AC$ (the length of the side opposite the 40° angle),
• $20$ is the hypotenuse $AB$,
• $\sin(40^\circ)$ represents the sine of the angle at $A$.

To solve for $b$, multiply both sides of the equation by 20:

$b = 20 \times \sin(40^\circ)$

Let's compute that.The length of $AC$ is approximately 12.9 cm when rounded to the nearest tenth.

Do you have any questions, or would you like further details?

Here are some related questions:

1. How do you calculate the sine of an angle in a right triangle?
2. How can we use trigonometric ratios to find unknown sides of a triangle?
3. What is the difference between sine, cosine, and tangent?
4. How would the problem change if the angle was 50° instead of 40°?
5. Can you explain how the sine function relates to the unit circle?

Tip: When solving trigonometric problems, always make sure your calculator is in the correct mode (degrees or radians) based on the angle's unit.