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To find the perimeter of triangle \( \triangle ABC \), we need to calculate the missing side \( x = BC \) and then add up the sides.

### Given Data:
- \( AB = 25 \)
- \( \angle A = 44^\circ \)
- \( \angle C = 39^\circ \)

### Step 1: Determine \( \angle B \)
Since the sum of angles in a triangle is \( 180^\circ \),
\[
\angle B = 180^\circ - 44^\circ - 39^\circ = 97^\circ.
\]

### Step 2: Use the Law of Sines
The Law of Sines states:
\[
\frac{AB}{\sin C} = \frac{AC}{\sin B} = \frac{BC}{\sin A}.
\]
We want to find \( BC = x \), so we'll use:
\[
\frac{x}{\sin A} = \frac{AB}{\sin C}.
\]

Plugging in the known values:
\[
x = AB \cdot \frac{\sin A}{\sin C}.
\]
Calculating \( \sin 44^\circ \) and \( \sin 39^\circ \):
\[
\sin 44^\circ \approx 0.694,
\]
\[
\sin 39^\circ \approx 0.629.
\]

Thus,
\[
x = 25 \cdot \frac{0.694}{0.629} \approx 25 \cdot 1.103 \approx 27.575.
\]

### Step 3: Calculate the Perimeter
Now that we have:
- \( AB = 25 \),
- \( AC = 25 \) (since no additional value for \( AC \) was provided),
- \( BC \approx 27.575 \).

The perimeter \( P \) is approximately:
\[
P = 25 + 25 + 27.575 \approx 77.575.
\]

### Answer
Rounding to the nearest whole number, the perimeter is approximately:
\[
\boxed{78}.
\]

Would you like additional details on any steps, or have any other questions?

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Here are 5 related questions:
1. How do you use the Law of Sines to find an unknown side in a triangle?
2. What other trigonometric laws are helpful in solving for sides and angles in triangles?
3. How can you find the perimeter of a triangle if two angles and one side are known?
4. What is the importance of rounding in trigonometric calculations?
5. How do different rounding methods affect the precision of results in trigonometry?

**Tip:** When working with trigonometric ratios, it's often best to use as many decimal places as possible initially and only round the final answer.

What is the perimeter of △ABC to the nearest whole number?

Learn how to find the perimeter of triangle ABC with given angles and sides using trigonometry and the Law of Sines. This example provides a step-by-step solution to calculate the missing side and find the perimeter, suitable for high school students.

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