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Geometry
Level
2
What will be the value of angle in degree between the hour hand and the minute hand when it is 2:17 a.m. in your watch? ?
The answer is 33.5.
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1 solution
The critical point here is to understand that hr hand and min. hand are not exactly at 2 and 17 respectively. In case of hr hand it was at 2 exactly at 2:00 but as time moves hr hand has to move to approach 3, it would not cover the entire distance in one moment it has to cover it during the 1 hour of time so its slightly ahead 2 that is 60º.
Angle traced by hour hand in 2 hrs 17 min. = 360/12 x (2 x 60+17)/60 º = 68.5º
Angle traced by min. hand in 17 min. = 360/60 x 17 º = 102º
Required angle = (102-68.5)º = 33.5º.
To the Author: According to me the answer should be 326.5º and not 33.5º as in the question its mentioned " between the hour hand and the minute hand " and we calculate the angle anti- clockwise beginning from the first vector in this case hr hand to the second vector that is min. hand so we'll be considering the outer angle and not the inner one. Please make the necessary correction.