Better Students Ask More Questions.
7. The big hand of a clock which measures 26.5 cm long and a small needlemeasures 15...
1 Answer | add yours
(Level 1) Associate Educator, Expert
At 2:30, the hour hand (shorter) is between 2 and 3, while the minute hand (longer) is at 6. The angle between numbers is `30^o` . From the midpoint of 2 and 3 to 3, we have `15^o` . Then, from 3 to 6 we have `3*30^o = 90^o` . Hence, the angle between the long and short hand is `90^0 + 15^o = 105^o` .
The length of the two hands in centimeters are `26.5cm` and `15*2.54 = 38.1 cm` . To get the length of the distance between the ends of the two hands, we simply use the Law of Cosine:
`c^2 = a^2 + b^2 - 2abcos(C)` where C is the included angle:
`c^2 = 26.5^2 + 38.1^2 - 2(26.5)(38.1)cos(105)`
`c^2 = 2676.493`
`c = 51.73cm`
Hence, the distance between the two ends is 51.73 cm.
Posted by mvcdc on July 7, 2013 at 12:45 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.