In a 30-60-90 triangle, the length of the side opposite the 30 angle is 8. find the length of the side opposite the 60 angle

Step-by-step explanation:

Let

x----> the side opposite the 60 angle

Applying the law of sines

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.