# The measure of an angle.

• May 12th 2008, 10:31 PM
NJDubois
The measure of an angle.
Ok, this has probably already been asked and solved; if so, please link me. Spent hours upon hours looking this up and I can't get anywhere.

In short, think of a clock; the hour hand is always at 12 and the second hand rotates around like normal.

What I know:
The radius of the circle and the length of the lines.

I need to know the formula for the angle measure where the hour hand and the second hand intersect?

A programmer who's eyes hurt.
• May 13th 2008, 12:23 AM
earboth
Quote:

Originally Posted by NJDubois
...

In short, think of a clock; the hour hand is always at 12 and the second hand rotates around like normal.
...
I need to know the formula for the angle measure where the hour hand and the second hand intersect?

....

Both hands point at the 12. Consider a period of 12 h. During this time the hour hand and the second hand (btw that's really a nice expression :D ) will meet

$\displaystyle (12 \cdot 60 - 1)$ times = 719 times

That means after $\displaystyle \frac1{719} \cdot 12\ hours$ the hand meat again. Since 1 hour is related to 30° with the hour hand the angle is:

$\displaystyle \frac1{719} \cdot 12 \cdot 30^\circ = \frac{360}{719}^\circ~\approx~ 0.50069541^\circ$

That's the angle the hour hand describes between two intersections.