To solve this problem and measure angle $\angle ACB$, we can proceed as follows:

Given:

• $AB = 7.2 \, \text{cm}$
• $AC = 3.5 \, \text{cm}$
• $\angle BAC = 28^\circ$

Steps to Determine $\angle ACB$

1. Apply the Law of Cosines to find the length of side $BC$. The formula for the Law of Cosines is: $BC^2 = AB^2 + AC^2 - 2 \times AB \times AC \times \cos(\angle BAC)$

   Substituting the values: $BC^2 = 7.2^2 + 3.5^2 - 2 \times 7.2 \times 3.5 \times \cos(28^\circ)$

   Calculating $BC$ will give us the third side of the triangle.

2. Apply the Law of Sines to find $\angle ACB$: The Law of Sines states: $\frac{\sin(\angle ACB)}{AC} = \frac{\sin(\angle BAC)}{BC}$

   Using the value of $BC$ obtained in step 1, you can rearrange and solve for $\angle ACB$: $\sin(\angle ACB) = \frac{AC \times \sin(28^\circ)}{BC}$

3. Calculate $\angle ACB$: Finally, take the inverse sine of the result to find $\angle ACB$ and round to the nearest degree.

Would you like me to perform the calculations explicitly, or would you prefer the conceptual approach laid out here?

Related Questions:

1. What is the length of side $BC$ after calculating it with the Law of Cosines?
2. How would we calculate $\angle ABC$ once we know $BC$?
3. Could this triangle be classified as an isosceles or scalene triangle based on the side lengths?
4. How would the angle $ACB$ change if $AC$ were longer or shorter?
5. What are some practical applications of using the Law of Sines and Cosines in real-world problems?

Tip:

When solving triangles, it’s useful to check that the sum of the angles equals 180° as a verification step.