91Ó°ÊÓ

The hour hand of an analog clock moves in proportion to the movement of the minute hand. This means that at \(4: 05,\) the hour hand will have moved beyond the 4 by \(\frac{5}{60}\) of the distance it would move in an hour. a) What is the measure of the obtuse angle between the hands of a clock at \(4: 00 ?\) Give your answer in degrees. b) What is the measure, in degrees, of the acute angle between the hands of a clock at \(4: 10 ?\) c) At certain times, the hands of a clock are at right angles to each other. What are two of these times? d) At how many different times does the angle between the hands of a clock measure \(90^{\circ}\) between 4: 00 and \(5: 00 ?\) e) Does one of the times occur before, at, or shortly after \(4: 05 ?\) Explain.