Question

Find the approximate length of EF.

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

Answer 1

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.