geometry/clock angles and degrees

[gonzo]

When the time is 2:18, how many degrees are there in the acute angle between the minute hand and the hour hand on a clock?

I know how to do the minutes: 360/60 = 6*18=108 degrees
Im stuck on hours: 360/12 = 30*2 = 60 degrees?????
108-60 = 48 degrees????

HELP!!

 

[stapel]

Hint: In one hour, the hour hand moves 1/12 of the way around the clock face. :wink:

Eliz.

 

[TchrWill]

When the time is 2:18, how many degrees are there in the acute angle between the minute hand and the hour hand on a clock?

The minute hand moves at the rate of 360º/60min = 6º/min.
The hour designations are 360º/12hr = 30º apart.
The hour hand moves at the rate of 30º/60min. = .5º/min.
I bet you can take it from here.

 

[soroban]

Hello, gonzo!

When the time is 2:18, how many degrees are there in the acute angle
between the minute hand and the hour hand on a clock?

I know how to do the minutes: \(\displaystyle \:\frac{360}{60}\:=\:6\;\;\Rightarrow\;\;6\cdot18\:=\:108^o\)
Im stuck on hours: \(\displaystyle \:\frac{360}{12}\:=\:30\;\;\Rightarrow\;\;30\cdot2\:=\:60^o\) ?
\(\displaystyle 108\,-\,60 \:= \:48^o\) ??
You forgot that the hour hand moves, too.

At exactly 2:00, the minute hand is at 0°; the hour hand is at 60°.
. . The angle is 60°.

By 2:18, the minute hand has moved 18 minutes: 108°.
. . And the hour hand has moved, too . . . to somewhere between "2" and "3".
Exactly where is it?

The hour hand was at "2" (60°). .In the next 18 minutes,
. . it moves \(\displaystyle \frac{18}{60}\) of the distance from "2" to "3" (30°):\(\displaystyle \;\frac{18}{60}\,\times\,30^o \:=\:9^o\)
Hence, the hour hand is at: .\(\displaystyle 60^o \,+\,9^o \:=\:69^o\)


Therefore, the angle is: \(\displaystyle \:108^o\,-\,69^o \:=\:\fbox{39^o}\)