Question

find in radian the angle between the hour hand and minute hand of a clock at (1) 10.40 AM (2) 3 hours 10 minutes

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{angle}\mathrm{between}\mathrm{the}\mathrm{hands}\mathrm{can}\mathrm{be}\mathrm{found}\mathrm{using}\mathrm{the}\mathrm{formula}, \\ △\mathrm{\theta }=\left|\frac{1}{2}\left(60\mathrm{H}-11\mathrm{M}\right)\right| \\ \mathrm{Here}\mathrm{it}\mathrm{is}10\mathrm{H}\mathrm{and}40\mathrm{M}\mathrm{so}, \\ △\mathrm{\theta }=\frac{1}{2}\left(60\times 10-11\times 40\right) \\ =80\mathrm{degree} \\ \mathrm{So}\mathrm{in}\mathrm{radian}=80\times \frac{\mathrm{\pi }}{180}=\frac{4\mathrm{\pi }}{9}\mathrm{radian} \\ \mathrm{Similar}\mathrm{approach}\mathrm{is}\mathrm{for}\mathrm{second}\mathrm{question}\mathrm{try}\mathrm{to}\mathrm{do}\mathrm{it}\mathrm{for}\mathrm{your}\mathrm{own}\mathrm{practice}. \end{gathered}$$