Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem27

11&12 Video Solutions 2011 problem27

Video Transcription

Video Summary

The problem involves finding non-congruent isosceles triangles with a base of 10 where the sine of one angle equals the cosine of another. By analyzing angle relationships, three cases arise. In the first two cases, setting the angles to specific values, only one valid triangle configuration is possible where alpha equals \(2\pi/3\) and beta equals \(\pi/6\). In the third case, a right isosceles triangle forms when beta equals \(\pi/4\) and alpha equals \(\pi/2\). Therefore, there are only two distinct non-congruent isosceles triangles possible, resulting in the answer.

Keywords

non-congruent isosceles triangles

angle relationships

sine cosine equality

triangle configurations

isosceles triangle cases