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.