Consider a simple clock.
a. Find the measure of the angle swept by the hour hand between noon and P.M.
b. Find the exact angle between the minute and hour hands at P.M.
a. The measure of the angle is .

Ask by John Cox. in the United States

Mar 22,2025

Question

Consider a simple clock.
a. Find the measure of the angle swept by the hour hand between noon and P.M.
b. Find the exact angle between the minute and hour hands at P.M.
a. The measure of the angle is .

Ask by John Cox. in the United States

Mar 22,2025

UpStudy AI · Accepted Answer

**a. Angle swept by the hour hand between noon and $$7{:}15$$ P.M.**

- The hour hand moves $$30^\circ$$ per hour.
- In 7 hours it moves:
  $$
  7 \times 30^\circ = 210^\circ.
  $$
- In 15 minutes (which is $$\frac{15}{60} = \frac{1}{4}$$ of an hour) it moves:
  $$
  \frac{1}{4} \times 30^\circ = 7.5^\circ.
  $$
- Total angle swept:
  $$
  210^\circ + 7.5^\circ = 217.5^\circ.
  $$
- Converting $$0.5^\circ$$ to minutes (since $$1^\circ = 60'$$):
  $$
  0.5^\circ \times 60' = 30'.
  $$
- Therefore, the measure of the angle is $$217^\circ 30'$$.

**b. Exact angle between the minute and hour hands at $$1{:}25$$ P.M.**

- **Minute hand:**
  - It moves $$6^\circ$$ per minute.
  - At 25 minutes past the hour, its position is:
    $$
    25 \times 6^\circ = 150^\circ.
    $$

- **Hour hand:**
  - It moves $$30^\circ$$ per hour.
  - At $$1{:}25$$ P.M., the hour hand has moved:
    - $$1$$ hour contribution: 
      $$
      1 \times 30^\circ = 30^\circ.
      $$
    - Plus additional movement due to 25 minutes:
      $$
      \frac{25}{60} \times 30^\circ = 12.5^\circ.
      $$
  - Total position of the hour hand:
    $$
    30^\circ + 12.5^\circ = 42.5^\circ.
    $$

- **Difference between the hands:**
  $$
  |150^\circ - 42.5^\circ| = 107.5^\circ.
  $$
- Converting $$0.5^\circ$$ to minutes:
  $$
  0.5^\circ \times 60' = 30'.
  $$
- Thus, the exact angle is $$107^\circ 30'$$.
**a. Angle swept by the hour hand between noon and $$7{:}15$$ P.M. is $$217^\circ 30'$$.** **b. Exact angle between the minute and hour hands at $$1{:}25$$ P.M. is $$107^\circ 30'$$.

Consider a simple clock.
a. Find the measure of the angle swept by the hour hand between noon and P.M.
b. Find the exact angle between the minute and hour hands at P.M.
a. The measure of the angle is .

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Consider a simple clock. a. Find the measure of the angle swept by the hour hand between noon and P.M. b. Find the exact angle between the minute and hour hands at P.M. a. The measure of the angle is .

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Consider a simple clock.
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