<p>Trapezoid <img alt="$ABCD$" height="13" src="https://latex.artofproblemsolving.com/f/9/e/f9efaf9474c5658c4089523e2aff4e11488f8603.png" width="57" /> has <img alt="$AD||BC$" height="18" src="https://latex.artofproblemsolving.com/8/3/4/834829da086ed651644d6091100aba2bc9611eee.png" width="68" />, <img alt="$BD = 1$" height="13" src="https://latex.artofproblemsolving.com/c/1/7/c17586f266d8a614e45964038dbd11de47c7389e.png" width="62" />, <img alt="$\angle DBA = 23^{\circ}$" height="13" src="https://latex.artofproblemsolving.com/2/9/8/298b55d1b105f19e8ec15cd3cf37c1dedce6ff52.png" width="105" />, and <img alt="$\angle BDC = 46^{\circ}$" height="13" src="https://latex.artofproblemsolving.com/b/9/c/b9ca5e8a969703d4b2af0f496dd416ed320f2ade.png" width="105" />. The ratio <img alt="$BC: AD$" height="13" src="https://latex.artofproblemsolving.com/6/f/c/6fc0676c527bea73515b0eeef409cd7154ac3a0e.png" width="72" /> is <img alt="$9: 5$" height="12" src="https://latex.artofproblemsolving.com/4/9/e/49e8520691de7e23593f5612af80aaa342b5f158.png" width="32" />. What is <img alt="$CD$" height="12" src="https://latex.artofproblemsolving.com/0/9/4/0948661e822f2a953c43a57ac9e40b2734476de4.png" width="29" />?</p>

Question No: 289

Trapezoid $ABCD$ has $AD||BC$ , $BD = 1$ , $\angle DBA = 23^{\circ}$ , and $\angle BDC = 46^{\circ}$ . The ratio $BC: AD$ is $9: 5$ . What is $CD$ ?

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Tags: Algebra Combinatorics Geometry Probability

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