Cannot solve Problems related to a Clock

[ConfusedPhysics]

"A clock has an hour hand that is 15.0 cm long, a minute hand that is 20.0 cm long, a secondhand that is 25.0 cm long."
"The time is 3 h 27 min 49 s"
"the hands are moving clockwise"
"for the hour hand calculate
1. speed of the hand
2. velocity of the hand at the given time"
"presume the hand from the the 12 position and find the change in
3. velocity,
4. average velocity,
5. average acceleration,
6. displacement"

The thing i am having the most trouble with is finding the central angle for the clock.

if i change time time into hours, it equals to 3.46 hours


if I multiply it by 30 to find the angle since each hour is 30 degrees to 12 o'clock it equals to 103.9 degrees.
but if i create a triangle using that number and the radius of the hour hand it will look like
this.
but this triangle does not make any sense since if solve for any of the other angles it will equal to
x= tan-1 (15/15)
x=45 degree
but that will make the angle equal to over 180 degrees, so i am confused on what i am supposed to do.1. The speed of the hour hand is the distance it goes divided by the time so
2*pi*r /(60*60)=v
v=7.6x10^-3 cm/s

2. the velocity of the given time is the magnitude of the speed so it is the same number but the i can't find the angle
V=7.6x10^-3 [some angle]

3. ∆v=(vf-vi)

∆v=(7.6x10^-3)^2+(-7.6x10^-3)^2-2(7.6x10^-3)(-7.6x10^-3)cos103.9
∆v=8.8x10^-5 cm/s

Its mostly the angle on what i am confused about

 

[SteamKing]

"A clock has an hour hand that is 15.0 cm long, a minute hand that is 20.0 cm long, a secondhand that is 25.0 cm long."
"The time is 3 h 27 min 49 s"

The thing i am having the most trouble with is finding the central angle for the clock.

if i change time time into hours, it equals to 3.46 hours

When the clock is at 3:00:00 exactly, the hands will appear like this: L

When the time is 3:27:49, I don't think the clock hands make the triangle as shown in your attachment.

if I multiply it by 30 to find the angle since each hour is 30 degrees to 12 o'clock it equals to 103.9 degrees.
but if i create a triangle using that number and the radius of the hour hand it will look like
this.
but this triangle does not make any sense since if solve for any of the other angles it will equal to
x= tan-1 (15/15)
x=45 degree
but that will make the angle equal to over 180 degrees, so i am confused on what i am supposed to do.

I'm not sure what you are doing here, but you can't treat this triangle like it was a right triangle. You have an oblique triangle, so you've got to use the law of sines or the law of cosines to figure out the missing information about the triangle.

 

[ConfusedPhysics]

Thank you so much, I completely forgot about that. I found the angles and the answers to the problem