Answer: The knights were responsible for protecting the people.
Answer: Yes
If I remember correctly, I believe these ordered pairs indicate a function, as there is exactly 1 output for every input (i.e., (output, input)). If there were 2 inputs of the same number, that'd make this relation not a function.
You want to end up with 
. Expand this using the angle sum identity for sine:
We want this to line up with 
. Right away, we know 
.
We also need to have
Recall that 
for all 
; this means
Then
So we end up with
It makes and obtuse right triangle.
Given:
10 yards required
5 2/3 yards on hand.
We need to subtract the yards on hand from the total yards required.
First, we need to convert the mixed fraction into an improper fraction.
5 2/3 = ((5*3)+2)/3 = (15+2)/3 = 17/3
Second, we need to multiply 10 by a fraction that will give us the denominator of 3.
10 * 3/3 = (10*3)/3 = 30/3
Third, we do subtraction using our derived fractions.
30/3 - 17/3 = (30-17)/3 = 13/3
Lastly, we simplify the improper fraction. Improper fraction is a fraction whose numerator is greater than its denominator. Its simplified form is a mixed fraction.
13/3 = 4 1/3
Arliss needs to buy 4 1/3 yards more to complete the required yard length.
