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To solve for the length \( b \) in the given triangle, we can apply the **Law of Sines**. The Law of Sines states:

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

Where:
- \( a = 27.2 \, \text{cm} \)
- \( A = 43^\circ \)
- \( B = 72^\circ \)
- \( C = 180^\circ - (43^\circ + 72^\circ) = 65^\circ \)

Now we can use the ratio:

\[
\frac{b}{\sin B} = \frac{a}{\sin A}
\]

Substitute the known values:

\[
\frac{b}{\sin 72^\circ} = \frac{27.2}{\sin 43^\circ}
\]

Solve for \( b \):

\[
b = \frac{27.2 \times \sin 72^\circ}{\sin 43^\circ}
\]

Using approximate values for the sine functions:

\[
b = \frac{27.2 \times 0.9511}{0.6820} \approx \frac{25.874}{0.6820} \approx 37.93
\]

To the nearest tenth of a centimeter, \( b \approx 37.9 \, \text{cm} \).

Would you like more details on this process or help with further steps?

Here are five related questions:
1. What is the Law of Cosines and when would you use it?
2. How would you calculate the length of side \( c \) in this triangle?
3. What are the applications of the Law of Sines in real-world problems?
4. How do you determine if a triangle is obtuse or acute?
5. Why is it important to know the sum of angles in a triangle?

**Tip:** Always ensure angle measurements are in degrees or radians as needed for trigonometric calculations.

Determine length b to the nearest tenth of a centimetre for the triangle with sides and angles: AB = 27.2 cm, ∠B = 72°, ∠C = 43°.

Learn how to determine the length of side b in a triangle using the Law of Sines. This problem involves a triangle with sides AB = 27.2 cm, ∠B = 72°, and ∠C = 43°. Find the solution step-by-step for students in Grades 10-11.

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