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Rufina [12.5K]
3 years ago
9

Trigonometry. I can't figure it out. ​

Mathematics
1 answer:
Ber [7]3 years ago
6 0

You also seem to be given that m\angle ADC=50^\circ, according to the diagram.

In triangle ABC, we have

\cos\angle CAB=\dfrac39=\dfrac13\implies m\angle CAB=m\angle CAD=\cos^{-1}\dfrac13

By the law of sines,

\dfrac{\sin\angle ADC}{AC}=\dfrac{\sin\angle CAD}{CD}

\implies CD=\dfrac{(9\,\mathrm{cm})\sin\left(\cos^{-1}\frac13\right)}{\sin50^\circ}\approx11.1\,\mathrm{cm}

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