Question

How do you find the length of the chord of a circle with radius 8 cm and a central angle of `110^@`?

Answer 1

You first draw a triangle connecting the ends of the chord (`A` and `B`) and the centre of the circle `C`.
You'll learn more if you make a drawing or scetch now.

Then you divide the chord in two equal halves and connect the middle `M` to the centre of the circle. You will see that you now have two equal (mirrored) triangles. It's easy to see (and prove) that both are rectangular at `M`.

Let's consider triangle `AMC`.
We know that the angle at `M` is now half of `110^0=55^0`
And we know that `AC=8` cm

`sin /_M=(AM)/(AC)->sin 55^0=(AM)/8->AM=8*sin55^0`

`AM=8*0.819...~~6.55` cm.