Math, asked by janhavipradhan942012, 1 year ago

Find the angle between hour hand and minute hand of clock at 20 minutes past two

Answers

Answered by mathdude500
1

Answer:

\boxed{\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \: =  \: 50^{ \circ}  \: }\\  \\

Step-by-step explanation:

We have to find the The angle between the minute hand and hour hand of a clock at 2:20.

We know,

\sf \: Angle\:subtended\:by\:minute\:hand \: in \: 1 \: hour =  {360}^{ \circ}  \\  \\

So,

\sf \: Angle\:subtended\:by\:minute\:hand \: in \: 60\: min =  {360}^{ \circ}  \\  \\

\sf \: Angle\:subtended\:by\:minute\:hand \: in \:1\: min =  {6}^{ \circ}  \\  \\

\sf \: Angle\:subtended\:by\:minute\:hand \: in \:20\: min =  {120}^{ \circ}  \\  \\

Now, Further, we know that

\sf \: Angle\:subtended\:by\:hour\:hand \: in \:12\: hours =  {360}^{ \circ}  \\  \\

\sf \: Angle\:subtended\:by\:hour\:hand \: in \:1\: hours =  {30}^{ \circ}  \\  \\

\sf \: Angle\:subtended\:by\:hour\:hand \: in \:2 \dfrac{20}{60} (= 2\dfrac{1}{3} =  \dfrac{7}{3}  ) \: hours =   \dfrac{7}{3} \times  {30}^{ \circ} = 70^{ \circ}  \\  \\

Now,

\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \:  \\  \\

\sf \:  =  \: 120^{ \circ} - 70^{ \circ} \\  \\

\sf \:  =  \: 50^{ \circ} \\  \\

Hence,

\implies\sf \: \boxed{\sf \: Angle\:between\:minute\:hand \: and \: hour \: hand \: =  \: 50^{ \circ}  \: } \\  \\

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