Question

Find the angle between the hour hand and the minute hand of a clock when the time is $3:25$.

Answer 1

Step 1: Convert the given time into hours

We are given the time $3:25$, that is, $3hr25min$

We know that there are $60$ minutes in an hour, so we can convert hours into minutes by dividing it with $60$

So, using unitary method,

$$\begin{gathered} 60min=1hr \\ \Rightarrow 1min=\frac{1}{60}hr \\ \Rightarrow 25min=\frac{25}{60}hr \end{gathered}$$

Thus, the time given is $(3+\frac{25}{60})hr=\frac{41}{12}hr$

Step 2: Evaluate the angle between the hands of the clock

We know that the hour hand completes one round around the clock in $12$ hours, that is, $360°$.

Apply the unitary method to evaluate the angle covered by the hour hand,

$$\begin{gathered} \Rightarrow 12hr=360° \\ \Rightarrow 1hr=\frac{360}{12}=30° \\ \Rightarrow \frac{41}{12}hr=30\times \frac{41}{12} \\ \Rightarrow \frac{41}{12}hr=\frac{205°}{2} \end{gathered}$$

Similarly, the minute hand will cover $360°$ in an hour.

So, again apply the unitary method to evaluate the angle covered by the minute hand,

$$\begin{gathered} \Rightarrow 1hr=360° \\ \Rightarrow 60min=360° \\ \Rightarrow 1min=\frac{360°}{60}=6° \\ \Rightarrow 25min=6\times 25 \\ \Rightarrow 25min=150° \end{gathered}$$

Thus, the angle between the minute hand and hour the hand will be $150°-\frac{205°}{2}=\frac{95°}{2}$

Hence, the required angle is $\frac{95°}{2}$.