Final answer:
Supplementary angles are pairs of angles whose sum is equal to 180 degrees, which is true. The Pythagorean theorem can be used to calculate the length of the resultant vector when two vectors are at right angles. However, without knowing magnitudes, we cannot determine the resultant angle of vector addition based solely on the angles of the original vectors.
Step-by-step explanation:
True or False: Supplementary angles are angles whose sum is equal to 180 degrees? The answer is A. True. Supplementary angles are indeed two angles whose measures add up to 180 degrees. An example of supplementary angles are two angles that form a straight line, where one angle can be 120 degrees and the other 60 degrees, and their sum is 180 degrees. Additionally, when working with vectors, the Pythagorean theorem can be used to calculate the length of the resultant vector for two vectors that are at right angles to each other, which is also true.
For the question about vector addition, we cannot necessarily determine the angle of the resultant vector if we only know the angles of the two vectors involved, without information about their magnitudes. This because the resultant's direction is dependent on both the magnitude and the angle of the individual vectors. The question as asked would be False. Additionally, a vector can indeed form the shape of a right angle triangle with its x and y components, which is how we often resolve vectors into their components in physics.
Regarding the range of a projectile, its range is equal to zero when the angle of projection is purely vertical, which means the angle would be 90 degrees. Any projectile launched straight up would fall back to its original launch point, resulting in a range of zero.