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Find the approximate length of EF.

A.
7.72 m
B.
14.6 m
C.
22.2 m
D.
27.48 m

Find the approximate length of EF. A. 7.72 m B. 14.6 m C. 22.2 m D. 27.48 m-example-1
User Chux
by
7.6k points

1 Answer

3 votes

Answer:

The correct option is B

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:


(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)

Using law of sine we get


(\sin D)/(d)=(\sin E)/(e)


(\sin D)/(EF)=(\sin E)/(DF)


(\sin 54^(\circ))/(EF)=(\sin 94^(\circ))/(18)


(0.809016994375)/(EF)=(0.99756405026)/(18)

Cross multiply,


0.809016994375* 18=0.99756405026* 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.

User Saidfagan
by
9.2k points

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