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Trigonometry
Question

In \( \triangle C D E , m \angle C \) is twice \( ...

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 \( D E ? \)

Answer

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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