A life preserver is seen floating down a river. The life preserver is first spotted 60 feet away. A few moments later the life preserver is 55 feet away, making a $40^{\circ}$ angle between the two sightings. How far did the life preserver travel? Round to the nearest tenth. Answer: feet

Step 1 ：Convert the angle from degrees to radians using the formula \(\gamma = 40 * \frac{\pi}{180} = 0.698\) radians

Step 2 ：Substitute the known values into the law of cosines: \(c^2 = 60^2 + 55^2 - 2 * 60 * 55 * \cos(0.698)\)

Step 3 ：Simplify the equation: \(c^2 = 3600 + 3025 - 6600 * \cos(0.698)\)

Step 4 ：Calculate the cosine and simplify further: \(c^2 = 6625 - 6600 * 0.766\)

Step 5 ：Subtract to find the value of \(c^2\): \(c^2 = 6625 - 5055.6 = 1569.4\)

Step 6 ：Take the square root of both sides to solve for c: \(c = \sqrt{1569.4} = 39.6\) feet

Step 7 ：The life preserver traveled approximately \(\boxed{39.6}\) feet