Chapter 12, Problem 24CR

a.

To determine

Find the angle formed by the clock hands.

Answer to Problem 24CR

  $165°$

Explanation of Solution

Given information:

  $At11:30$

Calculation:

A clock has total angle $360°$

Angle between two consecutive unit, $360°/12=30°$

  $At11:30$ the minute needle will be at $6$ and hour needle between $11and12$

The angle will be formed,

  $5.5\times 30=165°$

Hence, the angle formed by the clock hands be, $165°$ .

b.

To determine

Find the angle formed by the clock hands.

Answer to Problem 24CR

  $30°$

Explanation of Solution

Given information:

  $At2:05$

Calculation:

A clock has total angle $360°$

Angle between two consecutive unit, $360°/12=30°$

  $At2:05$ the minute needle will be at $1$ and hour needle be at $2$

The angle will be formed,

  $1\times 30=30°$

Hence, the angle formed by the clock hands be, $30°$ .

c.

To determine

Find the angle formed by the clock hands.

Answer to Problem 24CR

  $15°$

Explanation of Solution

Given information:

  $At3:24$

Calculation:

A clock has total angle $360°$

Angle between two consecutive unit, $360°/12=30°$

  $At3:24$ the minute needle will be between $4and5$ and hour needle be between $3and4$

The angle will be formed,

  $\begin{array}{l}4\times 30=120°\left[\min utehand\right]\\ 30\times 3\frac{1}{2}=105°\left[hourhand\right]\\ 120°-105°=15°\end{array}$

Hence, the angle formed by the clock hands be, $15°$ .