ABC is a triangle:

Angle A < 90.

D is a point on BC such that BD = DC.

M is a point on BC such that AM is perpendicular to BC.

If

AD = 10,

BC = 12 and

MC = 11
find the length of AC.

The problem gives us that angle A is acute. While we can use the law of cosines to solve for A and verify that statement, the important thing to know is whether angle C is acute. If angle C is obtuse, then MD is no longer 5, but is 16.

Unless that is the point: if the problem as Charadenine has broken it down and Friedlinguini has solved it requires angle A to be 90° or more, then we have the wrong triangle and must work with angle C being obtuse.

Posted by TomM on 2002-07-01 08:41:18