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.
Picture the triangle differently, and see if we can extrapolate an answer. Suppose angle A is not 20 degrees, but instead is 60 degrees. In that case, ABC would be equilateral, and point D would coincide with point C. Our answer for angle DBC would be zero degrees.
Now suppose instead, that angle A is very close to zero degrees. Then side BC would be nearly zero and the angles at C and B would be nearly 90 degrees, as would be angle DBC.
If angle A were 60, then answer would be 0
If angle A were 0, then answer would be 90
So, if angle A is 20, is then answer we want: 60 degrees??
(can anyone prove this is a linear relationship?)

Posted by Larry
on 20040908 07:45:17 