In the 30-60-90 triangle below, side s has a length of and side q has a length of

In a 30-60-90 triangle, the side lengths are in the ratio 1:2:sqrt(3) = short leg: hypotenuse: long leg.

We know the hypotenuse is 8. We can use this to find the other legs.

The short leg s is 8/2 = 4 because the short leg is always half of the hypotenuse.

The long leg q is 4 * sqrt(3), because the long leg is always sqrt(3) times the shorter leg.

So:

s = 4

q = 4 * sqrt(3)

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.

answer: the answer is 127 degrees