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Trigonometry
Question

In $$\triangle C D E , m \angle C$$ is twice $$m \angle D$$ and $$m \angle E$$ is $$3$$ times $$m \angle D$$ . If $$C D = 16 ,$$ what is $$D E ?$$

Let $$m\angle D= x$$

Then $$m\angle C= 2x$$   and   $$m\angle E= 3x$$

$$CD= 16$$ is opposite to $$m\angle E$$

$$DE$$ is opposite to $$m\angle C$$

$$\Rightarrow \frac { 16} { sin( 3x) } = \frac { DE} { sin( 2x) }$$

$$\Rightarrow DE= \frac { 16sin( 2x) } { sin( 3x) }$$

$$x+ 2x+ 3x= 180\Rightarrow x= 30°$$

$$∴ DE= 13.8564$$

Solution
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