Chapter 6, Problem 2CR

To determine

To Find: The angle formed by the hands of a clock at $9:30$

Answer to Problem 2CR

The angle formed by the hands of a clock at $9:30\text{ = 105}°$

Explanation of Solution

Given information:

We are given that the hands of the clock showing time $9:30$

Concept Used: A clock represents a circle so total angle is $360°$ in which angle made by minute hand in $1\text{ minute =6}°$ and angle made by hour hand in $1{\text{ hour = 30 }}^{°}$

Calculation:

Imagine the clock is showing 12:00 and starting from there counting the angle between the hands when it will reach $9:30$

For Hour Hand:

Angle covered by hour hand in $1$ hour = $30°$

Angle covered by hour hand in $9$ hours= $9\times 30°\text{ = 270 }°$

Angle covered by hour hand in $30$ minutes or $\frac{1}{2}$ hour = $\frac{1}{2}\times 30°\text{ = 15}°$

So total angle covered by hour hand till $9:30\text{ = 270}°\text{ + 15}°\text{ = 285}°\mathrm{................................}\text{(i)}$

For Minute Hand:

Angle covered by minute hand in $1$ minute = $6°$

Angle covered by minute hand in $30$ minute= $\text{6}°\times 30\text{ = 180 }°\mathrm{..........................................}\text{(ii)}$

Subtracting (ii) from (i) to get the final angle formed between the hands of clock at

  $9:30\text{ = 285}°\text{ - 180}°\text{ = 105}°$

Conclusion:

The angle formed by the hands of a clock at $9:30\text{ = 105}°$