Question

30 points! Find the length of side x in simplest radical form with a rational denominator.

Answer 1

2sqrt(3)

Explanation:

cos(30) = adjacent/hypotenuse

sqrt(3)/2 = x/4

x = 4 × sqrt(3)/2

x = 2sqrt(3)

sqrt: square root

Answer 2

2 sqrt(3) = x

Explanation:

We know that

sin theta = opp side / hypotenuse

sin 60 = x /4

Multiply each side by 4

4 sin 60 = x

We know

sin 60 = sqrt(3) /2

4 * sqrt(3) /2 = x

2 sqrt(3) = x