In 22, you're looking for the vertical height of the triangle. You're given the angle opposite the side you want to find (which I'll call
) and the length of the hypotenuse. This sets you up with the relation
In 23, you're given a similar situation, except now you're looking for the angle (I'll call it
) in the triangle opposite the side denoting the height of the airplane. So this time,
Part A: Explain why the x-coordinates of the points where the graphs of
the equations y = 4-x and y = 2x + 3 intersect are the solutions of the
equation
4-x = 2x + 3.
Because the point where the graphs intersect is a point that meets both rules (functions) y = 4 - x and y = 2x + 3 meaning that y from y = 4 - x equals y from 2x + 3 and also both x have the same value.
Part B: Make tables to find the solution to 4-x = 2x + 3. Take the integer values of x between -3 and 3.
x values 4 -x 2x + 3
-3 4-(-3)=7 2(-3)+3 =-3
-2 4-(-2)=6 2(-2)+3 =-1
-1 4-(-1)=5 2(-1)+3 = 1
0 4-0=4 2(0)+3 = 3
1 4-1=3 2(1)+3=5
2 4-2=2 2(2)+3 = 7
3 4-3=1 2(3)+3 = 9
The the solution is between x = 0 and x =1
Part C: How can you solve the equation 4-x = 2x + 3 graphically?
Draw in a same graph both functions y= 4 - x and y = 2x +3.
Then read the x-coordinates of the intersection point. That is the solution.
If you evaluate directly this function at x=0, you'll see that you have a zero denominator.
Nevertheless, the only way for a fraction to equal zero is to have a zero numerator, i.e.
So, this function can't have zeroes, because the only point that would annihilate the numerator would annihilate the denominator as well.
Moreover, we have
So, we can't even extend with continuity this function in such a way that 
11.k>-3(4r+3)/4r-5
12.k<(2x+2)/x+3
We can suggest this equation.
(6x+x)+(6x+x)+110º+110º=360º
7x+7x+220º=360º
14x=360º-220º
14x=140º
x=140º/14
x=10º
Answer. x=10º
