Can the isosceles triangle have an obtuse angle at the base?
No, it can’t. The property of a triangle: the sum of all angles in the triangle is equal to 180°. An isosceles triangle has two angles of the same measure at the base. So if it has an obtuse angle at the base, it has two obtuse angles. The obtuse angles – the angles which are larger than a right angle and smaller than a straight angle (between 90° and 180°) => their sum will be more then 180°. So a triangle can not contain two obtuse angles and thus it can’t have an obtuse angle at the base.