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The angles in a triangle add up to 180°.
\(m \angle D + m \angle E + m \angle F=180^\circ \\ 54^\circ + m \angle E + 32^\circ = 180^\circ \\ m \angle E=180^\circ - 54^\circ - 32^\circ \\ m \angle E=94^\circ\)

According to the law of sines, the ratio of the length of a side of a
triangle to the sine of the angle opposite to this side is the same for all sides.
So, the ratio of DF to sin m∠E is the same as the ratio of ED to sin m∠F.
\(\frac{18}{\sin 94^\circ}=\frac{x}{\sin 32^\circ} \\ \\ \frac{18}{\sin 94^\circ} \times \sin 32^\circ= x \\ \\ \frac{18}{0.9976} \times 0.5299 \approx x \\ \\ x \approx 9.56\)

The answer is C.

Answer:

The correct option is C. 9.56 meter

Step-by-step explanation:

∠D = 54° , ∠F = 32°

Now, Using angles sum property of a triangle

∠D + ∠F + ∠E = 180°

⇒ 54° + 32° + ∠E = 180°

⇒ ∠E = 180 - 86

⇒ ∠E = 94°

Now, Using sine rule in the triangle DEF

\(\frac{FD}{\sin 94}=\frac{ED}{\sin 32}\\\\\implies \frac{18}{\sin 94}=\frac{ED}{\sin 32}\\\\\implies ED = \frac{18 \times \sin 32}{\sin 94}\approx 9.56\text{ meter}\)

Hence, The correct option is C. 9.56 meter

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