#1**+2 **

We know sin 30 = 1/2

Sin also equals opposite side/hypotenuse

1/2 = sqrt(x/2) / 4x solve for x

2x=sqrt(x/2) square both side of the equation

4x^2 = x/2 Multiply by 2

8x^2 = x divide by 'x'

8x = 1 x = 1/8

ElectricPavlov Nov 2, 2018

#2**+1 **

In a 30 - 60 - 90 triangle....the side opposite the 30° angle is 1/2 the length of the hypotenuse....this implies that

sqrt ( x/ 2) / [ 4x] = 1/2 cross-multiply

2 sqrt (x / 2) = 4x divide both sides by 2

sqrt ( x /2) = 2x sqrare both sides

x / 2 = 4x^2 nmultiply both sides by 2

x = 8x^2 rearrange as

8x^2 - x = 0 factor

x ( 8x - 1) = 0

Setting each factor to 0 and solving for x produces

x = 0 [ reject ]

x = 1/8 [ accept ]

CPhill Nov 2, 2018