Final answer:
Vector a has a magnitude of 27 m and direction 32 degrees above the positive x-axis, while vector b has a magnitude of 35 m and direction 55 degrees below it. To estimate vector c's magnitude and direction, one must sketch and perform vector addition.
Step-by-step explanation:
The subject in question involves using analytical methods to determine the magnitude and direction of vector c = a + b, where vector a has a magnitude of 27 m and points 32 degrees above the positive x-axis, and vector b has a magnitude of 35 m and points 55 degrees below the positive x-axis. To estimate the magnitude and direction of vector c, start by sketching vector a and vector b according to their given magnitudes and directions. Then, perform vector addition by laying the tail of vector b at the head of vector a (or vice versa), and draw vector c from the tail of the first vector to the head of the last vector. Use a ruler and protractor to estimate the magnitude and direction angle of c from the sketch.