Question

given the description of the following triangles classify each one
a. triangle with angles: 37.5°, 105°, 37.5°
b. triangle with angles: 40°, 50°, 90°
c. triangle with angles: 60°, 40°, 80°

Explanation:

Step1: Recall triangle - type definitions

Triangles can be classified by angles as acute (all angles less than 90°), right (one angle equal to 90°), or obtuse (one angle greater than 90°). They can also be classified by side - length relationships as equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal). If two angles of a triangle are equal, it is isosceles.

Step2: Classify triangle a

The angles of triangle a are 37.5°, 105°, 37.5°. Since one angle (105°) is greater than 90°, it is an obtuse triangle. Also, since two angles (37.5° each) are equal, it is an isosceles triangle.

Step3: Classify triangle b

The angles of triangle b are 40°, 50°, 90°. Since one angle is 90°, it is a right triangle. Since all three angles are different, all three sides are different (by the law of sines), so it is a scalene triangle.

Step4: Classify triangle c

The angles of triangle c are 60°, 40°, 80°. Since all angles are less than 90°, it is an acute triangle. Since all three angles are different, all three sides are different, so it is a scalene triangle.

Answer:

a. Obtuse, Isosceles
b. Right, Scalene
c. Acute, Scalene