Answer:
A) 84
B) 84
C) 222
Explanation:
The angle between the hour hand and the minute hand is shown below.
Now the angle Θ is equal to the angle subtended by the hour clock with respect to 12 o'clock and the angle between 12 o'clock angle the minute hand.
Θ = | the minute hand - the hour hand |
A.
The angle between 12 o'clock and 8: 00 is
This angle is
[tex]\frac{8\colon\text{ 00}}{12\colon00}\cdot360[/tex]
in other words, 8 / 12 of a full circle.
The above simplifies to give
[tex]\frac{8\colon\text{ 00}}{12\colon00}\cdot360=240^o[/tex]
Now we find the angle between 12 o'clock and the minute hand.
This angle is
[tex]\frac{54}{60}\cdot360[/tex]
in other words, 54/60 of a full circle.
The above simplifies to give
[tex]\frac{54}{60}\cdot360=324^o[/tex]
Hence, the angle between the minute hand and the hour hand is
[tex]324-240=84^o[/tex]
The angle is 84 degrees.
B)
The angle we are looking for is shown in the sketch below.
The angle between 12 o'clock and 5: 00 is
[tex]\frac{5\colon\text{ 00}}{12\colon00}\cdot360=150^o[/tex]
Now we find the angle between 12 o'clock and the minute hand.
The angle between 12 o'clock and 11 minutes is
[tex]\frac{11}{60}\cdot360=66^o[/tex]
Therefore, the angle between the hands is
[tex]150^o-66^o=84^o[/tex]
The angle is 84 degrees.
C)
The angle we are looking for is shown in the sketch below.
The angle between 12 o'clock and 8:00 is
[tex]\frac{8}{12}\cdot360=240^o[/tex]
The angle between 12 o'clock and 3 minutes is
[tex]\frac{3}{60}\cdot360=18^o[/tex]
Therefore, the angle between the hands is
[tex]240^o-18^o=222^o[/tex]
The angle is 222 degrees.
Hence, to summerise
A) 84
B) 84
C) 222
