1. The radius of the circumscribed circle of the triangle ABC is 15 cm. Given that B is a 49-degree angle, find the length of side AC.
continuation - The radius of the circumscribed circle of the triangle ABC is r cm.
Given that B is a beta-degree angle, find the length of side AC, in terms of r and beta.
geometry - Reiny, Monday, April 12, 2010 at 11:34am
I don't know at what level of geometry you are starting, but a property of the circumscribed circle of a triangle is that
the diameter of the circumcircle is equal to the length of any side of the triangle divided by the sine of the opposite angle
so in your case the diameter is 15, and the required side AC is opposite angle B, so ...
15 = AC/sin49
AC = 15sin49
= appr. 11.32
Now do the same thing in the general case