Question

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Answer 1

Respuesta:

                  $\frac{10\sqrt{3} }{3}$

Explicación paso a paso:

Aplicando las razones trigonométricas en un triángulo rectángulo:

$Tan < A = \frac{BC}{AB}$       -----------   $Tan 30 = \frac{BC}{20}$  

$\frac{\sqrt{3} }{3} = \frac{BC}{20}$    -------------   $BC = \frac{20\sqrt{3} }{3}$

$Sen<A = \frac{BD}{AB}$   -------------   $Sen 30 = \frac{BD}{20}$

$\frac{1}{2} = \frac{BD}{20}$   ---------------------  $BD = \frac{20}{2} = 10$

Aplicando el teorema de Pitágoras:

$( BC)^{2} = ( BD)^{2} + ( DC)^{2}$  -----------  $( \frac{20\sqrt{3} }{3} )^{2} = ( 10 )^{2} + ( DC )^{2}$

$\frac{400(3)}{9} = 100 + (DC)^{2}$   ----------------  $\frac{1200}{9} -100 = (DC)^{2}$

$\frac{300}{9 } = ( DC)^{2}$  -------------           $\sqrt{\frac{300}{9} } = DC$

$\frac{10\sqrt{3} }{3} = DC$