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# Clock problem involving angles

I am studying for a geometry test and am having trouble with a review problem at the end of the chapter. This is not homework.

One problem asks the following: At 3:00, the hands of a clock form an angle of 90 degrees. To the nearest second, at what time will the hands of the clock next form a 90 degree angle? I figure that 4:05 is one time after three that the hands will form a 90 degree angle. So I figure that halfway betwee 3:00 and 4:05, the hands will form a right angle. Since half of 65 min is 32.5 minutes, so the answer should be 3:32:30. However, the answer at the end of the book is 3:32:44??? Don't understand this. The second part of the problem is: To the nearest second, what is the first time after 2:00 that the hands of a clock will form an angle 2.5 times as great as the angle formed at 2:00? The angle formed at 2 is 60 degrees. So we need the next time to form a 150 degree angle. The answer is 2:38:11. Not sure how to approach this.

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the ...

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