Answer:
Exercise 1: The length of the unknown leg is 4 inches. 
Exercise 3: The following straws can be used to construct the triangle: b)  , c)
, c)  , d)
, d)  , e)
, e)  , f)
, f) 
Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)
Step-by-step explanation:
Exercise 1:
Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:
 (1)
 (1)
Where:
 - Hypotenuse, in inches.
 - Hypotenuse, in inches.
 - Known leg, in inches.
 - Known leg, in inches.
 - Unknown leg, in inches.
 - Unknown leg, in inches.
If we know that  and
 and  , then the length of the unknown leg is:
, then the length of the unknown leg is:

Since 4 is the least whole number closest to  , then we conclude that the length of the unknown leg is 4 inches.
, then we conclude that the length of the unknown leg is 4 inches. 
Exercise 3: 
The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:
 (2)
 (2)
Where:
 - Greater side, in inches.
 - Greater side, in inches.
 - Lesser side, in inches.
 - Lesser side, in inches.
 - Missing side, in inches.
 - Missing side, in inches.
If we know that  and
 and  , then we have the following range of missing sides:
, then we have the following range of missing sides:

The following straws can be used to construct the triangle: b)  , c)
, c)  , d)
, d)  , e)
, e)  , f)
, f) 
Exercise 4:
Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:
(i) 

Possible choices: 5 inches.
(ii) 

Possible choices: 4 inches, 6 inches.
(iii) 

Possible choices: 5 inches, 6 inches.
(iv) 

Possible choices: None.
(v) 

Possible choices: 2 inches, 6 inches.
(vi) 

Possible choices: 5 inches.
(vii) 

Possible choices: None.
(viii) 

Possible choices: 2 inches, 4 inches, 10 inches.
(ix) 

Possible choices: 6 inches.
(x) 

Possible choices: 5 inches.
Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)