At what angle the hands of a clock are inclined at 15 minutes past 5?
58$ \dfrac{1}{2} ^\circ $
64$^\circ$
67$ \dfrac{1}{2}^\circ $
72$ \dfrac{1}{2} ^\circ $
Explanation:
Angle traced by hour hand in$ \dfrac{21}{4} $hrs =$\dfrac{360}{12}\times\dfrac{21}{4} ^\circ $=157$ \dfrac{1}{2} ^\circ $
Angle traced by min. hand in 15 min. =$ \left(\dfrac{360}{60} \times 15\right)^\circ $= 90$^\circ$.
$\therefore$ Required angle =$ \left(157\dfrac{1}{2} \right)^\circ $- 90$^\circ$ = 67$ \dfrac{1}{2} ^\circ $