17.2k views
12 votes
ABCD is a quadrilateral. Work out the length of CD. Give your answer to 3 significant figures

ABCD is a quadrilateral. Work out the length of CD. Give your answer to 3 significant-example-1
User Ceyhan
by
8.1k points

1 Answer

5 votes

Check the picture below.


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


\cfrac{sin(52^o)}{BD}=\cfrac{sin(102^o)}{CD}\implies CD=\cfrac{BD\cdot sin(102^o)}{sin(52^o)} \\\\\\ CD=\cfrac{(12)/(sin(35^o))\cdot sin(102^o)}{sin(52^o)}\implies CD=\cfrac{12\cdot sin(102^o)}{sin(35^o)\cdot sin(52^o)}\implies CD\approx 26.0

ABCD is a quadrilateral. Work out the length of CD. Give your answer to 3 significant-example-1
User Roozbubu
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories