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A triangle was dilated by a scale factor of 4. If tan a° = four thirds and segment FD measures 12 units, how long is segment EF?


triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees


segment EF = 6 units

segment EF = 9 units

segment EF = 12 units

segment EF = 16 units

Answer :

DunderMifflinite

Answer:

Segment EF = 16 units

Step-by-step explanation:

First we will figure out our equation:

Line FD is adjacent to angle a.

Line EF is opposite to angle a

and line ED is the hypotenuse.

Since we will being using Tangent, the hypotenuse is irrelevant.

Tan a° = [tex]\frac{opposite}{adjacent}[/tex]

Now substitute:

[tex]tan \frac{3}{4} = \frac{x}{12}[/tex]

Multiply both sides by 12:

[tex](12)tan\frac{3}{4} =x[/tex]

Solve for tangent by using your calculator:

[tex]tan \frac{3}{4}= 1.333333333[/tex]

[tex](12)1.333333333= 16[/tex]

[tex]16 = x[/tex]

EF = 16 units.

AndrewP02

Answer: the one above is correct

Step-by-step explanation:

Took the test!! :)

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