We can solve for $b$ using the Law of Sines, which is given by the formula:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

In this triangle:

• $a = 27$ (side opposite the angle $A = 28^\circ$)
• $A = 28^\circ$
• $B = 102^\circ$ (angle opposite the side $b$, which we need to solve for)
• $C = 50^\circ$ (since the sum of the angles in a triangle is 180°: $C = 180^\circ - 102^\circ - 28^\circ$)

To solve for $b$:

1. Use the Law of Sines to set up the equation: $\frac{27}{\sin 28^\circ} = \frac{b}{\sin 102^\circ}$

2. Solve for $b$: $b = \frac{27 \cdot \sin 102^\circ}{\sin 28^\circ}$

Let me calculate this for you.The length of side $b$ is approximately $56.3$ units when rounded to the nearest tenth.

Would you like more details on the steps, or do you have any other questions?

Here are five related questions to deepen your understanding:

1. How would you solve for the third side of the triangle using the Law of Cosines?
2. What happens if you have a triangle where you don’t know any angles?
3. How does the Law of Sines differ from the Law of Cosines?
4. Can the Law of Sines be applied to non-obtuse triangles?
5. How would you approach solving for side $b$ if the triangle were not solvable using the Law of Sines?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems.