A triangular swimming pool measures $44 \mathrm{ft}$ on one side and $32.4 \mathrm{ft}$ on another side. The two sides form an angle that measures $41.1^{\circ}$. How long is the third side? The length of the third side is $\square \mathrm{ft}$ (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.)

Step 1 ：We are given a triangular swimming pool with one side measuring 44 ft, another side measuring 32.4 ft, and the angle between these two sides is 41.1 degrees. We are asked to find the length of the third side.

Step 2 ：We can use the law of cosines to solve this problem. The law of cosines states that for any triangle with sides of lengths a, b, and c, and an angle γ opposite side c, the following equation holds: \(c^2 = a^2 + b^2 - 2ab\cos(γ)\)

Step 3 ：In this case, we know the lengths of sides a and b (44 ft and 32.4 ft, respectively), and the measure of angle γ (41.1 degrees). We can plug these values into the law of cosines to find the length of side c.

Step 4 ：Let's substitute the given values into the formula: \(c^2 = 44^2 + 32.4^2 - 2*44*32.4*\cos(41.1)\)

Step 5 ：Solving the above equation, we get \(c = \sqrt{28.934409547622884}\)

Step 6 ：Rounding to the nearest tenth, we get \(c = 28.9\) ft

Step 7 ：Final Answer: The length of the third side is \(\boxed{28.9}\) ft