+36916 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
+128474 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 ]
