Awire is to be attached to support a telephone pole. because of surrounding buildings, sidewalks, and roadways, the wire must be anchored exactly 18 feet from the base of the pole. telephone company workers have only 25 feet of cable, and 22 feet of that must be used to attach the cable to the pole and to the stake on the ground. how high from the base of the pole can the wire be attached?

The support wire is an illustration of Pythagoras theorem

The wire should be placed at 12.65 feet from the pole

The usable length of the wire is given as:

The wire must be anchored at 18 ft.

So, the height is:

The distance (d) from the height of the pole to the ground is illustrated using the following Pythagoras theorem

Substitute known values

Subtract 324 from both sides

Take square roots of both sides

Rewrite as:

Hence, the wire should be placed at 12.65 feet from the pole

Read more about Pythagoras theorem at:

link

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

c. side angle side. u shares the same sides