# Trigonometry word problem involving radius?

Can anyone show me how to solve this problem.

The radius of a circle is 21.4 meter. Find the length of the chord subtended by a central angle of 110 degrees 40 minutes and the distance between two parallel chords on the same side of the center subtended by central angles 118 degrees 40 minutes and 52 degrees 20 minutes.

-
What have you tried so far? –  Argon Jul 3 '12 at 21:34
Well I know the radius is 21.4 meter I set up a triangle but my final answer was wrong because I am not sure how to set it up. –  Fernando Martinez Jul 3 '12 at 21:35
draw perpendicular to the chord, the perpendicular will bisect the angle angle subtended at the center. –  Santosh Linkha Jul 3 '12 at 21:39
Please stop making titles that are descriptions followed by a question mark? –  rschwieb Jul 3 '12 at 23:45

## 1 Answer

Here is a hint:

You have $\dfrac{a}{r} = \sin \alpha$ and $\dfrac{b}{r} = \cos \alpha$.

You may have to take into account that some of these are half what you are interested in.

-
thank you for you illustration. –  Fernando Martinez Jul 3 '12 at 21:56
I see know that the length of the chord subtended by a central angle of 110 degrees 40 minutes is 35.2 thanks to your formula a/r sin a but I am having trouble doing the second part of my problem. –  Fernando Martinez Jul 3 '12 at 21:59
@Bishop: Try working out $b$ for both chords –  Henry Jul 4 '12 at 6:39