We multiply the area by 2 to solve for \( r \) because of the formula used to calculate the area of the triangle. The formula for the area of a triangle using two sides and the included angle is:

\[
\text{Area} = \frac{1}{2}ab \sin C
\]

In our problem:

- \( a \) and \( b \) are the distances \( OB \) and \( OC \), which are both equal to \( r \).
- \( C \) is the angle between \( OB \) and \( OC \), which is \( 62^\circ \).

Thus, the formula becomes:

\[
\text{Area} = \frac{1}{2} r^2 \sin 62^\circ
\]

Given that the area is 148 km², we set up the equation:

\[
148 = \frac{1}{2} r^2 \sin 62^\circ
\]

To isolate \( r^2 \), we multiply both sides of the equation by 2:

\[
2 \times 148 = r^2 \sin 62^\circ
\]

\[
296 = r^2 \sin 62^\circ
\]

Therefore, the multiplication by 2 is necessary to eliminate the fraction in the equation, making it possible to solve for \( r \).

Would you like more clarification or have any further questions?

### Additional Questions:
1. How is the formula for the area of a triangle derived?
2. Can this method be applied to non-right triangles? Why or why not?
3. What is the relationship between the sine function and the area of a triangle?
4. What other trigonometric functions can be used to find the area of a triangle?
5. How does the value of the sine function change with different angles?
6. What would the effect be if the angle \( C \) were obtuse?
7. Why do we use radians instead of degrees in some calculations?
8. How would the calculation change if the area were given in different units?

### Tip:
Always remember to double-check your work when converting between different trigonometric function representations, such as degrees and radians, as mistakes can easily lead to incorrect calculations.

Explore how to calculate the area of a triangle using two sides and the included angle. This problem involves applying trigonometric principles to solve for the triangle's area, with detailed steps and a clear explanation. Suitable for high school students studying geometry and trigonometry.

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