Suppose we have a triangle with sides of length 3, 4, and 5 units. We can use the Pythagorean theorem to verify that this triangle is a right triangle: 3^2 + 4^2 = 9 + 16 = 25 = 5^2. Therefore, the angle opposite the side of length 5 is a right angle. We can also use the Law of Cosines to find the measure of one of the acute angles in the triangle. Let A, B, and C be the vertices of the triangle, with side AB of length 3, side BC of length 4, and side AC of length 5. Let angle C be the angle opposite the side of length 5. Then, by the Law of Cosines, we have cos(C) = (3^2 + 4^2 - 5^2) / (2 * 3 * 4) = -1/8. Since C is acute, we know that cos(C) is positive, so we take the absolute value to get cos(C) = 1/8. Therefore, we have C = arccos(1/8) ≈ 82.62 degrees.