Chapter 1.4, Problem 9PSA

To determine

To find: The angle between the hands of the clock at 11:40.

Answer to Problem 9PSA

The angle between the hands of the clock at 11:40 is $110°$ .

Explanation of Solution

Given:

Hands of a clock showing the time either 11:40 am or 11:40 pm.

Concept Used:

  $\begin{array}{l}12\text{hour}=360°\\ 1\text{hour}=\frac{360°}{12}=30°\\ 1\text{minute}=\frac{30°}{60}=\left(\frac{1}{2}\right)°\end{array}$

Also, the formula for exact angle between hands of a clock hh:mm

  $\theta =\left|\frac{11}{2}\times \text{minutes}-30\times \text{hour}\right|$

Calculation:

As per the given problem time is 11:40, thus the angle between hands of clock is

  $\begin{array}{l}\theta =\left|\frac{11}{2}\times \text{40}-30\times \text{11}\right|\\ \text{=}\left|\text{220}-330\right|\\ =\left|-110\right|\\ \therefore \theta =110°\end{array}$

Conclusion:

  $\theta =110°$