Do you know which theorems needed to solve this problem Question : Con sider all the triangles you can create using the points shown below as vertices. Note, we are notallowing degen er ate triangles (ones with all three vertices on the same line). How many non-right triangles can youcreat e? Please explain your thinking and your answer in great detail as st ated in the guidelines of this project.11@へ @ 小ENG11/thing

The objective here is to find the number of non-right triangles that can be created using the dots above as vertices. Note that a triangle need three vertices to form.Here the total number of vertices are= Horizontal vertices+ vertical vertices=7+4=11 Now, for to form a triangle first find the number of ways of choosing three vertices out of the given 11. C311=11!11−3!3!=11×10×9×8!8!3×2×1=11×5×31=165Now, since collinear points can not form a triangle, so find that the chosen vertices are collinear and subtract them from total in order to find the vertices to make the triangle.Number of ways to chose collinear vertices can be find as=All three of them are horizontal + All three of them are vertical C37+C34=7!7−3!3!+5!5−3!3!=7×6×5×4!4!3×2×1+5×4×3!2!3!=35+5×42×1=35+10=45 Note that the total vertical points are 5(one corner point that is included in horizontal as well.) Now the number of ways to form a non-right angle triangle is=Total number of ways of choosing three vertices-number of ways of choosing 3 collinear vertices =165-45=120 Note that since the corner point is included in both cases when finding the ways of choosing collinear vertices, i.e. the triangle formed will be non-right triangle.Answer: There are 120 ways to form a non-right angle triangle from given points. Explanation for answer: To form a triangle using certain number of given points(vertices) three non-collinear vertices are required, and in order to form non-right triangle the corner vertices(joining horizontal and vertical vertices) should not be included. Here such number of ways are 120 only. (Note that here knowledge for permutation and combination is needed)