Find the angle between the hands of a clock at 5:15A 60B 67.5C 75

Accepted Solution

Answer:Option B is correct.67.5 degreeStep-by-step explanation:To find the angle between the hands of a clock.Given that: Hands of a clock at 5 : 15.We know that:A clock is a circle and it always contains 360 degree.Since, there are 60 minutes on a clock.[tex]\frac{360^{\circ}}{60 minutes} = 6^{\circ} per minutes[/tex]so,  each minute is 6 degree.The minutes hand on the clock will point at 15 minute,then, its position on the clock is:[tex](15) \cdot 6^{\circ} = 90^{\circ}[/tex]Also, there are 12 hours on the clock⇒Each hour is 30 degree.Now, can calculate where the hour hand at 5:00 clock.⇒[tex]5 \cdot 30 =150^{\circ}[/tex]Since, the hours hand is between 5 and 6 and we are looking for 5:15 then :15 minutes is equal to [tex]\frac{1}{4}[/tex] of an hour⇒[tex]150+\frac{1}{4}(30) = 150+7.5 = 157.5^{\circ}[/tex]Then the angle between two hands of clock:⇒[tex]\theta = 150.75 -90 = 67.5^{\circ}[/tex]Therefore, the angle between the hands of a clock at 5: 15 is: 67.5 degree.