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 Nov 2, 2018
 #1
avatar+18360 
+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  

 Nov 2, 2018
 #2
avatar+100579 
+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 ]

 

 

cool cool cool

 Nov 2, 2018

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