Gougu Rule for the right triangles is the Chinese Pythagorean theorem. In the late age of the Chosun Dynasty, mathematicians of Chosun pioneered the study of the Chinese Nine Chapters and other advanced mathematical problems as well as the Easternism in spite of the various difficulties after the Imchinoeran(임진왜란), Chungyuchairan(정유재란) and Byungchahoran(병자호란) The technologies of the addition and addition twice are the methods of the solution of the problems in the right triangles. This paper is intended to introduce some problems using these methods of solution.