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To solve this problem, we need to find the distances from tower A and tower B to the fire using trigonometry, specifically the Law of Sines or Law of Cosines.

### Step 1: Analyze the Triangle Formed
The points in the diagram form a triangle:
- Let \( A \) be the position of tower A,
- \( B \) be the position of tower B, which is 60 miles away from A,
- \( C \) be the position of the fire.

The angles provided are:
- \( \angle CAB = 40^\circ \), which is the angle between the line from A to B and the line from A to C.
- The direction angles help determine the interior angles of the triangle:
  - From the directions given, we can find the angle \( \angle ABC \) as \( 323^\circ - 324^\circ = 1^\circ \).
  - The angle \( \angle ACB \) would then be \( 180^\circ - (40^\circ + 1^\circ) = 139^\circ \).

### Step 2: Use the Law of Sines
With angle \( \angle ACB = 139^\circ \), side \( AB = 60 \) miles, and angle \( \angle CAB = 40^\circ \), we can apply the Law of Sines:

\[
\frac{AC}{\sin(1^\circ)} = \frac{60}{\sin(139^\circ)}
\]

Solving this equation for \( AC \) will give the distance from tower A to the fire.

Let me calculate that.The fire is approximately 2 miles from tower A. 

Would you like further details or have any questions?

Here are some related questions:
1. How can we find the distance from the fire to tower B?
2. What if the directions were different; how would that change the calculations?
3. How is the Law of Sines applied in non-right triangles?
4. Why is it important to round to whole numbers in distance calculations?
5. Can the Law of Cosines be used here instead of the Law of Sines?

**Tip:** In trigonometric problems, always double-check angle measures, as they are crucial for accurate results.

A ranger in tower A spots a fire at a direction of 324°. A ranger in tower B, located 60 mi at a direction of 40° from tower A, spots the fire at a direction of 323°. How far from tower A is the fire? How far from tower B?

Learn how to use the Law of Sines to find the distance from tower A to a fire spotted at an angle of 324° and 323° from two different towers. This trigonometry problem involves analyzing angles and applying the Law of Sines to solve for unknown distances. Suitable for high school students in Grades 10-12.

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