Consider a regular pentagon with edge length A as in Figure 2. The diagonals of the pentagon form a star-shaped figure called a penta- gram. It was the ancient symbol of the Pythagorians and played a major role in the rites of mystical and occult societies of medieval times, a role which continues today. a. Show that the length of the diagonal AC, and hence of each diagonal, is p, where Hint: Use the Law of Sines on the triangle AABC and the fact that sin 3/5 = sin/5.] b. Determine the three smaller angles at a vertex of the pentagon. (ie. ZABP, 4PBQ, LQBC) c. Calculate the ratios: AC AQI and AQ TAPI B - A: Figure 2