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To solve for side \( b \) in this triangle, we can use the Law of Sines. Given that we know:

- \( m\angle A = 56^\circ \)
- \( m\angle B = 73^\circ \)
- \( a = 10 \)

### Step 1: Find \( \angle C \)
Since the sum of angles in a triangle is always \( 180^\circ \), we can find \( \angle C \) as follows:

\[
m\angle C = 180^\circ - m\angle A - m\angle B
\]
\[
m\angle C = 180^\circ - 56^\circ - 73^\circ = 51^\circ
\]

### Step 2: Apply the Law of Sines
The Law of Sines states:

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

To find \( b \), we can rearrange it as:

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

Substitute the known values:

\[
b = 10 \cdot \frac{\sin 73^\circ}{\sin 56^\circ}
\]

Using approximate values for the sines of these angles:
- \( \sin 73^\circ \approx 0.9563 \)
- \( \sin 56^\circ \approx 0.8290 \)

\[
b = 10 \cdot \frac{0.9563}{0.8290}
\]

\[
b \approx 10 \cdot 1.1535
\]

\[
b \approx 11.5
\]

### Final Answer:
\[
b \approx 11.5
\]

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. How does the Law of Sines help in solving triangles with missing sides?
2. What would be the process if we were asked to solve for side \( c \) instead?
3. Can you solve for angle \( C \) directly using only given angles \( A \) and \( B \)?
4. How would the solution change if \( a \) had a different value?
5. Why is it important to round to the nearest tenth in this type of problem?

**Tip:** Always check that all angles add up to 180° in a triangle to verify calculations.

Given: m∠A = 56°, m∠B = 73°, a = 10. Find: b. Round your answer to the nearest tenth.

Learn how to solve for side b in a triangle with given angles A=56°, B=73°, and side a=10 using the Law of Sines. This problem provides a step-by-step solution, covering key trigonometric concepts and the angle sum property. Suitable for students in Grades 10-12.

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