Answer:
Right Scalene Triangle
Explanation:
Definitions:
Angles
Acute angle: An angle whose measure is less than 90 degrees.
Right angle: An angle whose measure IS 90 degrees. As a consequence, the two rays that form the angle are perpendicular.
Obtuse angle: An angle whose measure is greater than 90 degrees.
Triangles (defined by side lengths)
Equilateral Triangle: A triangle with all three sides congruent (all three sides have the same length)
Isosceles Triangle: A triangle that contains two congruent sides (two sides with the same length).
Scalene Triangle: A triangle with three different length sides.
Triangles (defined by angle measures)
Acute Triangle: A triangle whose angles are all acute angles
Right Triangle: A triangle that contains one right angle.
Obtuse Triangle: A triangle that contains one obtuse angle.
Analyzing our triangle:
By angle
Our triangle has an angle that appears to be a right angle (the two sides look perpendicular). This would be a Right Triangle (when classified by angles).
By side length
All three sides of this triangle are different in length. This would be a Scalene Triangle (when classified by side length).
Combining the attributes:
This is both a Right Triangle and a Scalene Triangle. Together, it is a Right Scalene Triangle.
Analyzing the other options given:
Right Isosceles
To be a Right Isosceles Triangle, the triangle needs to be both a Right Triangle, and an Isosceles Triangle.
A Right triangle contains one right angle, and an Isosceles Triangle contains a pair of sides that are the same length.
While this triangle does contain a right angle, all three sides appear to be different length (scalene).
This is not a Right Isosceles Triangle.
Acute Isosceles
To be an Acute Isosceles Triangle, the triangle needs to be both an Acute Triangle, and an Isosceles Triangle.
An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and an Isosceles Triangle contains a pair of sides that are the same length.
However, this triangle contains a right angle (equal to 90 degrees, not less than), so it cannot be an Acute Triangle, and this triangle does not contain a pair of sides that are the same length, so it cannot be an Isosceles Triangle.
This is not an Acute Isosceles Triangle.
Acute Scalene
To be an Acute Scalene Triangle, the triangle needs to be both an Acute Triangle, and a Scalene Triangle.
An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and a Scalene Triangle has sides that are all different length.
While this triangle does have sides that are all different length, it contains a right angle, whose measure IS 90 degrees (not less than 90 degrees). So it cannot be an Acute Triangle
This is not an Acute Scalene Triangle.