From the trivia question Math SATs #295: I'm planting 8 trees in a circle so that they are all equally spaced. If the radius of this circle is 5 m, how far would each tree be from the tree next to it (in a direct line)?
Tue, 21 Jul 2009 22:48:56 -0000
There are two ways to do this.
The simple way is to realize that the circumference of a radius 5 circle is about 31. Since we have 8 trees, we have 7 spaces between them, so dividing the whole circumference into spaces between each tree gives a bit more than 4, which means the direct linear distance should be around 4.
The more formal way is to use cosine law- draw a triangle between two trees and the centre. The angle between the two radius-sides of length 5 will be 360/7, or about 51 degrees, so you have two sideds and the angle between them, just plug it into the cosine law and you get about 4.