Question

answer
scalene right
equilateral
isosceles obtuse
scalene acute
scalene obtuse
isosceles acute
isosceles right

Explanation:

Step1: Check side - lengths

The side - lengths of the triangle are 4.05, 4.05, and 6.09. Since two side - lengths are equal (4.05 and 4.05), it is an isosceles triangle.

Step2: Check angle measures

We are not given angle measures directly, but we can use the Pythagorean theorem for right - triangles. Let \(a = 4.05\), \(b = 4.05\), and \(c = 6.09\). Calculate \(a^{2}+b^{2}=4.05^{2}+4.05^{2}=16.4025 + 16.4025=32.805\) and \(c^{2}=6.09^{2}=37.0881\). Since \(a^{2}+b^{2}
eq c^{2}\), it is not a right - triangle. Also, since \(c^{2}>a^{2}+b^{2}\), the angle opposite the side \(c\) is obtuse.

Answer:

Isosceles Obtuse