https://file.aiquickdraw.com/mathbot/file/1725110805959y1o7v7rq.jpg

Round your answer to the nearest hundredth.

The image you provided shows a right triangle with a 40-degree angle at \( B \), a right angle at \( C \), and sides labeled \( AC \), \( AB \), and \( BC \). The lengths of sides \( AB \) and \( BC \) are both marked as 7 units. We need to calculate the length of \( AC \) and round the answer to the nearest hundredth.

### Step 1: Identify the sides
- \( AB = 7 \) (Hypotenuse)
- \( BC = 7 \) (Opposite to the 40° angle)
- \( AC \) (Adjacent to the 40° angle)

### Step 2: Use the sine or cosine function
To find \( AC \), we'll use the cosine function because it relates the adjacent side to the hypotenuse:
\[
\cos(40^\circ) = \frac{AC}{AB}
\]

### Step 3: Solve for \( AC \)
\[
AC = AB \times \cos(40^\circ)
\]
Substitute the value of \( AB = 7 \):
\[
AC = 7 \times \cos(40^\circ)
\]

Let's calculate this.The length of side \( AC \) is approximately \( 5.36 \) units when rounded to the nearest hundredth.

Do you want more details on the calculation or have any further questions?

Here are some related questions you might consider:
1. How would you find the length of side \( BC \) using trigonometric functions?
2. How do you calculate the area of this triangle?
3. Can you verify the length of \( AC \) using the Pythagorean theorem?
4. How does the sine function relate to side \( BC \) and angle \( B \)?
5. What are some real-world applications of right triangle trigonometry?

**Tip:** When solving triangle problems, always check if multiple methods (like trigonometry and the Pythagorean theorem) can be used to verify your results.

Learn how to calculate the length of side AC in a right triangle with a 40-degree angle using trigonometric principles. This problem involves using the cosine function to relate the adjacent side to the hypotenuse. Suitable for high school students.

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