Respuesta :

JonHenderson55
The correct answer is:  [C]:  " 5√3 " .
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Explanation:
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In a "30-60-90" triangle: 

The side opposite from the "30° angle" is "x" ; 

The side opposite from the "60° angle is:  "x√3" ; 

and the "hypotenuse"  is:  "2x" ; 
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So, from the "image attached":  

The side opposite from the "60° angle is:  "x√3" ; which equals: " 15 " (given) ;  
So, x√3 = 15 ; 

Divide each side by "√3" ; to isolate "x" on one side of the equation ; 
 & to solve for "x" ; 

(x√3) / √3  =  15 / √3 ; 

x = 15 / √3 ;  

→  Multiply the entire equation by "√3/√3" (which equals "1"); to get ride oif the "square root" in the "denominator" ; 

→   " 15 / √3  =  (15 *√3) / (√3 * √3) " ;

                   = (15√3) / 3 ;  
 
                   =  5√3 ; which is:  Answer choice:  [C]:  " 5√3 " .
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crisforp

So, tan30 = x / 15;

Then, [tex] \frac{\sqrt{3}}{3} = \frac{x}{15} ;
x = \frac{15\sqrt{3}}{3};
x = 5\sqrt{3}.
[/tex]

The correct answer is : [tex] 5\sqrt{3} . [/tex]

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