A triangular traffic island has sides \( 21.9,14.3 \), and 13.4 . What are the angles at the comers? The angle across from the side 21.9 is \( 104.4^{\circ} \). (Round to the nearest tenth as needed.) The angle across from the side 14.3 is \( 39.2^{\circ} \). (Round to the nearest tenth as needed.) The angle across from the side 13.4 is \( \square^{\circ} \) (Round to the nearest tenth as needed.)

To find the third angle of the triangular traffic island, we can use the fact that the sum of all angles in a triangle is \(180^\circ\). We already have the angles across from side \(21.9\) as \(104.4^\circ\) and across from side \(14.3\) as \(39.2^\circ\). Now, we can calculate the third angle: \[ \text{Third angle} = 180^\circ - (104.4^\circ + 39.2^\circ) = 180^\circ - 143.6^\circ = 36.4^\circ. \] Thus, the angle across from the side \(13.4\) is \(36.4^\circ\). If you ever find yourself needing to identify angles in triangles but only have the lengths of the sides, you can utilize the Law of Cosines for precise results. This formula helps you find the angles based on the sides of the triangle, eliminating the guesswork and ensuring accuracy. Just remember to round your answers carefully to maintain clarity! For further exploration, consider diving into the world of triangle properties—like those found in Euclidean geometry. You'll discover fascinating relationships like congruence and similarity, which can aid not only in theoretical math but also in practical applications like architecture and engineering. There's so much beauty and utility in triangles, as they form the basic building blocks of many structures!