The image in the book is very small, so you need to be accurate with your measurements.
On the diagrams below, the gray squares indicate the corner of a sheet of notebook paper. Since this corner is a right angle, you can use this simple tool to compare the angles of the diagram to 90 degrees.
If the paper corner hides the angle, then the angle measure is less that 90 degrees. Therefore, the angle is acute.
If the paper corner fits perfectly in the angle, then the angle is a right angle.
If you cannot cover the whole angle with the paper corner, then the angle measure is more than 90 degrees. Therefore, the angle is obtuse.
The diagrams also show rulers to measure the length of the sides. The tick marks on these rulers are at 116, 18, 316, 14, 516, 38, 716, 12,... inches.
Let's look at the triangles one by one.
Triangle 1
Classification by Side Length
The length of the three sides are approximately 516, 38, and 12 inches. These are all different, so this is a scalene triangle.
Classification by Angles
Two angles are covered by the paper corner, so these are acute.
The paper corner closely fits in the third angle, but we still cannot cover it. This third angle is slightly obtuse. Since the triangle has an obtuse angle, it is an obtuse triangle.
Triangle 2
Classification by Side Length
The length of the shortest side is approximately 316 inches. One of the other sides is a bit more than 716, inches, while the third one is a bit less than 716 inches. These are all different, so this is a scalene triangle.
Classification by Angles
Two angles are covered by the paper corner, so these are acute.
The paper corner fits perfectly in the third angle, so it is a right angle.. Since the triangle has a right angle, it is a right triangle.
Triangle 3
Classification by Side Length
The length of the three sides is approximately 14, 516, and 12 inches. These are all different, so this is a scalene triangle.
Classification by Angles
Two angles are covered by the paper corner, so these are acute.
The paper corner does not cover the third angle, therefore this third angle is obtuse. Since the triangle has an obtuse angle, it is an obtuse triangle.
Triangle 4
Classification by Side Length
The lengths of the three sides are approximately 916, 516, and 916 inches. Two of these are the same, so this is approximately an isosceles triangle.
Classification by Angles
All angles are covered by the paper corner, therefore all three of the angles are acute.
Since all angles are acute, this is an acute triangle.
Triangle 5
Classification by Side Length
The lengths of the three sides are approximately 316, 1 116, and a bit less than 1 116 inches. These are all different, so this is a scalene triangle.
Classification by Angles
Two angles are covered by the paper corner, therefore these are acute.
The paper corner fits perfectly in the third angle, so it is a right angle. Since the triangle has a right angle, it is a right triangle.
Triangle 6
Classification by Side Length
The lengths of the three sides are approximately 38, 1516, and 1316 inches. These are all different, so this is a scalene triangle.
Classification by Angles
Two angles are covered by the paper corner, so these are acute.
The paper corner does not cover the third angle, therefore this third angle is obtuse. Since the triangle has an obtuse angle, it is an obtuse triangle.
