Question

select the best classification for the triangle by its angles and sides. obtuse, isosceles obtuse, equilateral obtuse, scalene right, isosceles

Explanation:

Step1: Analyze side - length relationships

The side - lengths of the triangle are \(4.2\), \(r\), and \(2r\). Since the three side - lengths \(4.2\), \(r\), and \(2r\) are all different (assuming \(r
eq4.2\) and \(r
eq 2.1\)), the triangle is a scalene triangle.

Step2: Analyze angle relationships

One angle is given as \(30^{\circ}\). If it were a right - triangle, with one angle \(30^{\circ}\), the sides would follow the ratio \(1:\sqrt{3}:2\). But our side - length ratios are not in this form. Also, since one angle is \(30^{\circ}\), and the sum of angles in a triangle is \(180^{\circ}\), and the triangle is not a right - triangle, the other non - \(30^{\circ}\) angles must make the third angle obtuse.

Answer:

Obtuse, scalene