Answer:
The correct option is B
Step-by-step explanation:
Given information: ∠F=32°,∠D=54° and DF=18m.
According to the angle sum property of triangle, the sum interior angles of a triangle is 180°.
Using angle sum property, we get
\(\angle D+\angle E+\angle F=180^{\circ}\)
\(54^{\circ}+\angle E+32^{\circ}=180^{\circ}\)
\(\angle E+86^{\circ}=180^{\circ}\)
\(\angle E=180^{\circ}-86^{\circ}\)
\(\angle E=94^{\circ}\)
Law of sine:
\(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\)
Using law of sine we get
\(\frac{\sin D}{d}=\frac{\sin E}{e}\)
\(\frac{\sin D}{EF}=\frac{\sin E}{DF}\)
\(\frac{\sin 54^{\circ}}{EF}=\frac{\sin 94^{\circ}}{18}\)
\(\frac{0.809016994375}{EF}=\frac{0.99756405026}{18}\)
Cross multiply,
\(0.809016994375\times 18=0.99756405026\times EF\)
Divide both sides by 0.99756405026.
\(EF=14.5978655656\)
\(EF\approx 14.6\)
The value of EF is 14.6 m. Therefore the correct option is B.
