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
[tex]\angle D+\angle E+\angle F=180^{\circ}[/tex]
[tex]54^{\circ}+\angle E+32^{\circ}=180^{\circ}[/tex]
[tex]\angle E+86^{\circ}=180^{\circ}[/tex]
[tex]\angle E=180^{\circ}-86^{\circ}[/tex]
[tex]\angle E=94^{\circ}[/tex]
Law of sine:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
Using law of sine we get
[tex]\frac{\sin D}{d}=\frac{\sin E}{e}[/tex]
[tex]\frac{\sin D}{EF}=\frac{\sin E}{DF}[/tex]
[tex]\frac{\sin 54^{\circ}}{EF}=\frac{\sin 94^{\circ}}{18}[/tex]
[tex]\frac{0.809016994375}{EF}=\frac{0.99756405026}{18}[/tex]
Cross multiply,
[tex]0.809016994375\times 18=0.99756405026\times EF[/tex]
Divide both sides by 0.99756405026.
[tex]EF=14.5978655656[/tex]
[tex]EF\approx 14.6[/tex]
The value of EF is 14.6 m. Therefore the correct option is B.
