Question

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Answer 1

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`\sin( 35^o )=\cfrac{\stackrel{opposite}{12}}{\underset{hypotenuse}{BD}} \implies BD\sin(35^o)=12\implies BD=\cfrac{12}{\sin(35^o)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill`

`\cfrac{CD}{\sin(102^o)}=\cfrac{BD}{\sin(52^o)}\implies CD\sin(52^o)=BD\sin(102^o) \\\\\\ CD=\cfrac{BD\sin(102^o)}{\sin(52^o)}\implies CD=BD\cfrac{\sin(102^o)}{\sin(52^o)} \\\\\\ CD=\cfrac{12}{\sin(35^o)}\cdot \cfrac{\sin(102^o)}{\sin(52^o)}\implies CD\approx 25.969~cm`

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