What is the distance between the points a and b on the flagpole? explain how you got your answer using the trigonometric functions!

Hello!

Let's think of this large triangle as a whole. If we add up the angles, we have 115°. The adjacent side to this angle is 9 feet. Let's try finding the opposite side. The tangent deals with these two.

tan115≈2.14

Therefore, x/9=2.14

We multiply both sides by 9 to find x.

x=19.26

Now let's find the length BC and subtract it from 19.26 to find our length. As we will deal with opposite and adjacent sides, we will find the tangent.

tan45=1

This means x/9=1

Therefore, BC=9

Now we can subtract from 19.26

19.26-9=10.26

Therefore, this length is 10.26 feet

I hope this helps!

the answer to the question is a  

it has the same slope and the same y-intercept.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: