Question

Find in radians, the angle between the hour hand and the minute hand of a clock at half past three.

• A. $5\pi /12$
• B. $7\pi /12$
• C. $11\pi /12$
• D. $3\pi /12$

Answer 1

Answer: (A)

The angle traced by the hour hand in $12$ hrs $=360^{\circ }$
$\therefore$ The angle traced by the hour hand in $3$ hrs $30$ mins
i.e., $\frac{7}{2}hr={\left(\frac{360}{12}\times \frac{7}{2}\right)}^{\circ }=105^{\circ }$
The angle traced by the minute hand in $60$ mins $=360^{\circ }$
$\therefore$ The angle traced by the minute hand in $30$ mins
$={\left(\frac{360}{60}\times 30\right)}^{\circ }=180^{\circ }$
Hence, the required angle between two hands
$=180^{\circ }-105^{\circ }=75^{\circ }$
Required angle in radians $=\left(75\times \frac{\pi }{180}\right)=\frac{5\pi }{12}rad$