Question 1042617: This is one question but it is extremely long. If you can, please explain it thoroughly. Thanks for you help and time in advance!
A geometry teacher sent her students home with an assignment to analyze some lists of given side lengths—a, b, and c— to determine if each list of side lengths could form a triangle. And if a triangle was possible for any of the given lists, to draw a diagram of the triangle and label it with sides a, b, and c, and angles A, B, and C as shown below (side a opposite angle A, B opposite B, and c opposite C.)
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/43.1-HOT2-Tris.jpg
The student was then asked to determine which angle was smallest and which was largest and to explain their reasoning. The teacher gave three lists to each student. Look at each student’s list,
Caroline got the following three lists:
List 1:
a = 6
b = 4
c = 5
List 2:
a = 10
b = 25
c = 13
List 3:
a = 6
b = 15
c = 17
Caroline’s answer looked like this:
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/43.1-HOT2-Tris2.jpg
List 1: Angle A = largest; Angle C = smallest
The numbers in list 1 are all close enough that they can make a triangle. Angle A is the largest because it is across from the longest side, so the other two sides have to be spread wide enough to reach it. Angle C is the smallest because it is across from the smallest side so it can’t reach very far.
List 2: These numbers cannot make a triangle because 25 is too long and 10 & 13 can’t reach the ends of the 25 side.
List 3: Angle C = largest; Angle A = smallest
The lengths of this triangle are all close enough to make a triangle because 2 long sides can connect to a short side unlike List 2 where there were 2 short sides. Angle C is the largest because it is across from the longest side. Angle A is the smallest because it is across from the shortest side.
Graziella got the following three lists:
List 1:
a = 14
b = 2
c = 22
List 2:
a = 16
b = 5
c = 11
List 3:
a = 8
b = 9
c = 6
Graziella’s answer looked like this:
https://byuis.brainhoney.com/Resource/46824921,0/Assets/Media/Images/43.1-HOT2-Tris3.jpg
List 1: No, c is too long 22. Side b is too short 2. It would not be a triangle.
List2: B has the smallest angle because b is the smallest side. A is the largest because a 16 is the longest side, so A has a wider angle.
List 3: This can be a triangle because of the length of each side. B has the largest angle because the opposite side b is longer, therefore, since c is shorter, the angle should open more in order for b and c to touch. On the other hand, C has the smallest angle because c is shorter, therefore, C doesn’t open as wide as the other angles.
a. Critique the work of Graziella and Caroline. What did they do right? What did they do wrong?
b. What grade would you give Graziella and Caroline for this assignment? Why?
c. What clarifications can you add to their work to make their answers more worthy of a top grade?
Answer by ikleyn(52772)   (Show Source):
You can put this solution on YOUR website! .
If you divide/separate this list in "n" independent assignments, where n is sufficiently large number,
you probably will get answers for some of them.
When you send it as the whole list (almost infinite) your chances to get the answer are extremely low.
It is so obvious . . .
You can do not thank me for this advise.
It is free of charge.
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