Final answer:
The statement is false; a triangle can have at most one obtuse angle because the sum of angles in any triangle is always 180 degrees.
Step-by-step explanation:
The statement that some triangles can have more than one obtuse angle is false. By definition, an obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. Since the sum of the angles in any triangle must equal 180 degrees, having more than one obtuse angle would exceed this total, making it impossible. Therefore, a triangle can have at most one obtuse angle.
The concepts referenced by the additional statements relate to vector mathematics and geometry. The Pythagorean theorem is used to calculate the length of the resultant vector when adding two vectors at right angles to each other. Furthermore, knowing the magnitudes and angles of two vectors does not necessarily determine the angle of the resultant vector unless the vectors are at a right angle to each other. However, if the magnitude and direction of one vector and the angles of both are known, it is possible to find the magnitude and direction of the resultant vector. This methodology can be akin to triangulation, a process used in geometry to determine distances, as referenced in Figure 19.4.