Suppose you have a right triangle and draw a line that bisects the triangle into two smaller triangles. If one of the triangles has an area that is three times more than the other, what are the angles of this triangle?
It's a poorly worded question, but I'm going to assume that its the right angle that's bisected rather than the triangle, (the normal interpretation of the triangle being bisected would be that it's divided into two equal parts, in which case how can one of the smaller triangles be three times the size of the other ?).
So, if that assumption is correct, suppose that the lengths of the two sides making up the right angle are a and b, (with say a greater than b), and that the length of the bisecting line from the right angle across to the hypotenuse is c, then the areas of the two small triangles will be a*c*sin(45)/2 and b*c*sin(45)/2. If the first of these areas is three times the second, (a>b), it follows that a = 3b so a/b = 3, and that will be the tangent of one of the angles of the original triangle,
