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)

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: