Question

What is the angle between the hours hand and minutes hand of a clock at (i) 1.40 hours, (ii) 2.15 hours? (Use $1^o=60$ minutes.)

Answer 1

$60min$ hand rotates ${360}^o$

$1mm=\frac{360}{60}=6^o$

$60min$ rotates ${30}^o$

In $1min$ it will rotate $\frac{30}{60}={\frac{1}{2}}^o$

(a) Here $x={210}^o$

$x=z+y\Rightarrow 210=z+20$

$\therefore z={190}^o$

At suppose hour hand will move $y^o$ from 1.

$1min$ hour hand moves by ${\frac{1}{2}}^o$

$\therefore$ In $40min$ hour hand will move $40\times \frac{1}{2}=2$

$\therefore y={20}^o$

(b) Here $x={30}^o$

$x=z+y$

In $15min$ hour hand will move $=5\times \frac{1}{2}=7.5$

$\Rightarrow 30=z+7.5$

$\therefore z={22.5}^o$