Question

at $2\!:\!48$ what is the degree measure of the smaller angle formed by the hour and minute hands of a $12$-hour clock?

Answer 1

Angle between hour and minute hand= 61°

The hour hand has covered 2 h and 22 min from position 12 o'clock (reference position). And in case of minute hand 22 min from reference. Required angle is angle covered by minute hand minus the angle covered by hour hand (clearly minute hand has covered greater angle in comparison with hour hand).

For calculating angle covered by minute hand:

In 60 min the min hand covers 360°

60 min = 360°

1 min = 6° ; 22 min = 132°

For calculating angle covered by hour hand:

12 h ( of hour hand) = 360°

1 h = 30°

For [2 + (22/60)] h, the angle covered= [2 + (22/60)]*30° = 71°

Angle between hour and minute hand = (132–71)° = 61°

It is the acute angle between hour and minute hand. For finding reflex angle subtract the obtained acute angle from 360°. So the reflex angle will be 299°.

Angle between hour and minute hand= 61°

learn more about Angle: brainly.in/question/3469466

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