Triangle ABC has side AB=AC, and angle BAC = 20 degrees.

D is a point on side AC with AD=BC. Find angle DBC.

Solve this without trigonometry.

Firstly Draw the shape above, without the triangle ABD, as accurately as possible.

Then, rotate about point B until BC is on line BD.
Keep on doing this until Point A on the copied drawing lines up exactly with point A on the original.

Then use the formula 360/(No. of steps/No of rotations) to give the angle DBC.

This is an untidy way, but the result would be correct.

Posted by Juggler on 2004-09-07 19:17:00