Chapter 11.1, Problem 76E

Numerical and Graphical Analysis Forces with magnitudes of 180 newtons and 275 newtons act on a hook (see figure). The angle between the two forces is θ degrees.

(a) When $\theta =30°$, find the direction and magnitude of the resultant force.

(b) Write the magnitude $M$ and direction $\alpha$ of the resultant force as functions of θ, where $0°\le \theta \le 180°$.

(c) Use a graphing utility to complete the table.

θ	0°	30°	60°	90°	120°	150°	180°
M
α

(d) Use a graphing utility to graph the two functions $M$ and $\alpha$.

(e) Explain why one of the functions decreases for increasing values of θ, whereas the other does not.