Find the measure (in radians) of a central angle of a sector of area 13 square inches in a circle of radius 2.5 inches. The central angle measures approximately radians. (Round to the nearest tenth.)

Step 1 ：We are given that the area of the sector is 13 square inches and the radius of the circle is 2.5 inches. We are asked to find the measure of the central angle in radians.

Step 2 ：The formula for the area of a sector of a circle is \( A = \frac{1}{2} r^2 \theta \), where \( r \) is the radius of the circle, \( \theta \) is the central angle in radians, and \( A \) is the area of the sector.

Step 3 ：We can rearrange this formula to solve for \( \theta \): \( \theta = \frac{2A}{r^2} \)

Step 4 ：Substituting the given values into this formula, we get \( \theta = \frac{2 \times 13}{(2.5)^2} \)

Step 5 ：Solving this equation, we find that \( \theta \approx 4.2 \)

Step 6 ：Final Answer: The measure of the central angle of the sector is approximately \(\boxed{4.2}\) radians.