MTH 112: Project 5 You will need a miler, a protractor, and a piece of bland paper. questions using complete sentences. Clearly write measurement the you make. 1. Draw a quadrilateral on your paper. Three of the sides should measure 8 em, while the last side will measure some other amount. The fret side should be horizontal. It should look something like this D (a) Go CCW around the exterior of your figure and label the four vertices with the letters A. B.C. D. You should do this so that the side from D to A is the side that is not 8 em long. (b) Label each of the four sides as vectors AB. BC, CD, DA. Draw an arrowhead to indicate the direction of each vector. (c) Measure each of the four sides. (Three of them should be 8 em if you followed the directions!) (d) Measure the exterior angle at each corner. Here's a picture so you can see what is meant by an exterior angle. The exterior angle at point B is 0, the exterior angle at point C Is . 2. Draw two coordinate axes and carefully redraw the four vectors so that they all begin at the origin. The vector AB should be on the r-axis. (a) If you drew the vectors carefully you should notice that the angle between AB and BC is the same as the exterior angle you measured at point B. The angle between BC and CD is the exterior angle you measured at point C. and so forth. (Notice that this tells you that the exterior angles should add to 360 degrees). Use your knowledge of vectors and the circular functions to find a Cartesian representation for each of these vectors. (b) What should the sum of these four vectors be? (Hint: Look back at your first drawing!) (e) Find the sum of your four vectors. (d) Are your two answers the same? 3. Draw the diagonals from point A to point C' and from point B to point D. (a) Measure these diagonals. (b) Find vector expressions for the diagonals AC and BD and then cal- culate the Cartesian form of these two vectors. (c) Do the magnitudes of the vectors you found match the diagonal lengths you measured