geometry homework help!!!

Question

Find the measure of the angle formed by the hands of a clock at each time.

3:00

4:30

7:20

1:45

Answer 1

A circular clock has 360°

At 3:00 the angle is 90°

Since 3/12=1/4 of a circle  360°/4 = 90°

4.30

The angle between two numbers is 360/12 = 30°

The angle betwee 4.30 is halfway between 4:00 and 5:00. 30°/2=15°

At 4:30 the angle is 30 + 15=45°

Answer 2

The formula for the angle between hour hand and minute hand

Answer 3

The formula for the angle between hour hand and minute hand θ = | 30H - 5.5M |.

where:

• is the angle in degrees of the hand measured clockwise from the 12 o'clock position.
• is the hours past 12 o'clock.
• is the minutes past the hour.
• is the minutes past 12 o'clock.

The time is 3 : 00.

The angle between two hands (hour hand and minute hand) θ = | 30H - 5.5M | = | 30(3) - 5.5(00) | = 90^o.

 

The time is 4 : 30.

The angle between two hands (hour hand and minute hand) θ = | 30H - 5.5M | = | 30(4) - 5.5(30) | = | 120 - 165 | = 45^o.

 

The time is 7 : 20.

The angle between two hands (hour hand and minute hand) θ = | 30H - 5.5M | = | 30(7) - 5.5(20) | = | 210 - 110 | = 100^o.

 

The time is 1 : 45.

The angle between two hands (hour hand and minute hand) θ = | 30H - 5.5M | = | 30(1) - 5.5(45) | = | 30 - 247.5 | = 217.5^o.

Answer 4

The little(hour) hand isn't always on the exact number. It moves in sync with the minute hand, only on a smaller scale.

Since there's 360 degrees in a clock, the angle between each hour number is 30 degrees.

To find out how much it has moved, take 30 degrees (for the full hour) and multiply it by the number of minutes divided by 60.

1) The time is 3:00.

The hour hand is at 3 and the minute hand is at 12. There are 3 hour numbers between them and there is no moment in the hour hand so tthe angle is 3 * 30° = 90 degrees.

2) The time is 4:30.

There are 2 hour numbers between 4 and 6. But the hour hand 4 is moved with some angle in 30 minutes.

To find out how much it has moved, take 30 degrees (for the full hour) and multiply it by the number of minutes divided by 60.

Angle of movement of the little(hour) hand is 30° * (30/60) = 30° * (1/2) = 15°

That means the hour hand has moved 15 degrees past the 4 in 30 minutes.

The angle between 4 and 5 is 30° but 15° is moved so the remaining angle is 30° - 15° = 15°

The angle between 5 and 6 is 30°.

So at 4:30 the angle is 15° + 30° = 45°.

3) The time is 7:20.

There are 3 hour numbers between 7 and 4. But the hour hand 7 is moved with some angle in 20 minutes.

To find out how much it has moved, take 30 degrees (for the full hour) and multiply it by the number of minutes divided by 60.

Angle of movement of the little(hour) hand is 30° * (20/60) = 30° * (1/3) = 10°

That means the hour hand has moved 10 degrees past the 7 in 20 minutes.

The angle between 4 and 5 is 30°.

The angle between 5 and 6 is 30°.

The angle between 6 and 7 is 30°.

Angle moved from 7 in 20 minutes is 10°.

So at 7:20 the angle is 30° + 30° + 30° + 10° = 100°.

4) The time is 1:45.

There are 8 hour numbers between 1 and 9. But the hour hand 8 is moved with some angle in 45 minutes.

To find out how much it has moved, take 30 degrees (for the full hour) and multiply it by the number of minutes divided by 60.

Angle of movement of the little(hour) hand is 30° * (45/60) = 30° * (3/4) = 22.5°

That means the hour hand has moved 22.5 degrees past the 1 in 45 minutes.

The angle between 1 and 2 is 30°. But angle moved is 22.5°. So the remaining angle is 30° - 22.5° = 7.5°.

Angle moved from 1 in 45 minutes is 7.5°.

The angle between 2 and 3 is 30°.

The angle between 3 and 4 is 30°.

The angle between 4 and 5 is 30°.

The angle between 5 and 6 is 30°.

The angle between 6 and 7 is 30°.

The angle between 7 and 8 is 30°.

The angle between 8 and 9 is 30°.

So at 1:45 the angle is 7.5° + 30° + 30° + 30° + 30° + 30° + 30° + 30° = 217.5°.