SOLUTION: The hour hand of a clock is 4 inches long while the minute hand is 5 inches long. At some time between 12:15 PM and 12:30 PM, the tips of the hands are 8 inches apart. What time

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: The hour hand of a clock is 4 inches long while the minute hand is 5 inches long. At some time between 12:15 PM and 12:30 PM, the tips of the hands are 8 inches apart. What time       Log On

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 Question 160353: The hour hand of a clock is 4 inches long while the minute hand is 5 inches long. At some time between 12:15 PM and 12:30 PM, the tips of the hands are 8 inches apart. What time is it then? (Answer to the nearest second.)Answer by ankor@dixie-net.com(15649)   (Show Source): You can put this solution on YOUR website!The hour hand of a clock is 4 inches long while the minute hand is 5 inches long. At some time between 12:15 PM and 12:30 PM, the tips of the hands are 8 inches apart. What time is it then? (Answer to the nearest second.) : Find the angle (A) between the hands using the law of cosines: : b^2 + c^2 -2(bc)Cos(A) = a^2 Let a=8, b=4, c=5 : 4^2 + 5^2 - 2(4*5)Cos(A) = 8^2 16 + 25 - 2(20)Cos(A) = 64 41 - 40Cos(A) = 64 -40Cos(A) = 64-41 Cos(A) = A = 125.1 degrees is the angle between the hands : Let m = minutes hand position : 6m = degrees per min : Hour hand moves 360/12 = 30 degrees per hr : An equation Hrs degrees + 125.1 degrees = minutes degrees *30 = 125.1 = 6m : + 125.1 = 6m Multiply equation by 2 m + 250.2 = 12m : 250.2 = 12m - m : 250.2 = 11m m = m = 22.927 min or 22 min + .927(60) = 22 min 56 sec