The questions is to find the radius of a wonder building. It is basically just an arc. It says the span is 30 meters and the height is 10. I drew a line along the base of the arc and made that my x axis and drew a line up the centre finding my y axis. I found the centre by placing two random chords and bisecting them and where the lines meet it's my centre. I'm trying to find the radius. The answer is 16.25m but I dont know how to find it. Please help, I'm Usually good at this type of stuff and I'm sad because I can't figure it out. I bet there is something real simple that I'm just forgetting. Any who thank you!
-
http://s562.photobucket.com/albums/ss68/…
15^2 + (r-10)^2 = r^2
225 + r^2 – 20r + 100 = r^2
20r = 325
r = 16.25
15^2 + (r-10)^2 = r^2
225 + r^2 – 20r + 100 = r^2
20r = 325
r = 16.25
-
sounds like you have a great start!
the base (x-axis in your diagram is bisected) has segments of length 15 each.
let x be the length from the bisection to the other side of the circle. That is, 10 + x is the length of the chord (and is also the diameter)
so 15∙15 = 10∙x (intersecting chords theorem)
giving x = 22.5
so the diameter (10+x) is 32.5
and the radius is half the diameter, or 16.25
hope that helps
the base (x-axis in your diagram is bisected) has segments of length 15 each.
let x be the length from the bisection to the other side of the circle. That is, 10 + x is the length of the chord (and is also the diameter)
so 15∙15 = 10∙x (intersecting chords theorem)
giving x = 22.5
so the diameter (10+x) is 32.5
and the radius is half the diameter, or 16.25
hope that helps