Final answer:
Angle 3 is a right angle because line L is perpendicular to line n, meaning they intersect at 90 degrees. In trigonometry and vector calculations, this perpendicularity forms the basis for determining angles and magnitudes using the Pythagorean theorem and trigonometric ratios.
Step-by-step explanation:
The reason for the conclusion that Angle 3 is a right angle, based on the given information that line L is perpendicular to line n, is due to the definition of perpendicular lines. In geometry, when two lines are perpendicular, they intersect to form four right angles. Therefore, if line L is perpendicular to line n, any angle formed at the intersection of these two lines will be a right angle, which is exactly 90 degrees.
To further elaborate, envision this scenario using vectors and trigonometry, where vectors form a right triangle and one angle is known to be 90 degrees because of the perpendicular relationship between the lines. This fact aids in calculating various properties of the scenario, such as vector magnitudes and directions, through the application of the Pythagorean theorem and trigonometric ratios like the sine, cosine, and tangent functions.