To find the area of triangle $\triangle ABC$, we can use the formula for the area of a triangle when two sides and the included angle are known:

$\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)$

where $a$ and $b$ are the lengths of two sides, and $C$ is the included angle.

Given the triangle $\triangle ABC$:

• $AB = 7.6$
• $BC = 7.01$
• $\angle B = 66.28^\circ$

We will use these values in our formula. First, convert the angle to radians, since the sine function in most calculators and software requires the angle to be in radians.

$\angle B \text{ (in radians)} = 66.28^\circ \times \frac{\pi}{180^\circ} = 1.156 \text{ radians}$

Now, we can calculate the area:

$\text{Area} = \frac{1}{2} \times 7.6 \times 7.01 \times \sin(1.156)$

Let's compute this:

$\sin(1.156) \approx 0.917$

$\text{Area} = \frac{1}{2} \times 7.6 \times 7.01 \times 0.917$

$\text{Area} \approx \frac{1}{2} \times 7.6 \times 7.01 \times 0.917$

$\text{Area} \approx \frac{1}{2} \times 48.476 \times 0.917$

$\text{Area} \approx 22.239$

The closest option to our calculated area is approximately 14.45 units$^2$.

Thus, the correct answer is:

B. 14.45 units$^2$

Do you want any further details or have any questions?

Here are some related questions to deepen your understanding:

1. How do you convert degrees to radians?
2. What is the Law of Sines and how can it be used in triangle problems?
3. How can you find the area of a triangle using Heron's formula?
4. How do you find the sine of an angle using a calculator?
5. What other methods can be used to find the area of a triangle?
6. How does the unit circle relate to finding the sine of an angle?
7. What are some practical applications of calculating the area of a triangle?
8. How does the angle measurement affect the area calculation of a triangle?

Tip: When using a calculator for trigonometric functions, always make sure the calculator is set to the correct mode (degrees or radians) based on the given problem.