Question

In △DEF, what is the length of DF ?

A. 54
B. 18 sqrt 3
C. 27 sqrt 2
D. 9 sqrt 3

Answer 1

a 30-60-90 triangle is pretty standard, do you know the dimensions of the usual one?

Answer 2

no

Answer 3

do you know how to use trig ratios?

Answer 4

sin cos tan ??

Answer 5

yes

Answer 6

27/DF = sin60

Answer 7

so how do i solve it

Answer 8

sin60 = sqrt(3)/2
Now you can solve it

Answer 9

you determine which trig ratio you can use with the given information

Answer 10

notice that we have an angle, and that we are given a side across from it, and are asked to find the hypotenuse

trig(angle) = over and hypotenuse; is there a trig function we could apply with this information?

Answer 11

scaling the usual 30-60-90 would be simpler, but its also good to know how to apply the trigs :)

Answer 12

sin??

Answer 13

sin is correct; sin is defined as over/hypot; lets call the hypot, "x" for simplicity

sin(60) = 27/x

Answer 14

an equilateral triangle has 3 60 degree angles such that we can determine the measurements of these

Answer 15

the sqrt(3) correspond to our 27 measure; so consider the multiplier "n" such that

n sqrt(3) = 27

then all the other sides mulitply the same:

1*n = the bottom measure
and 2*n = the slant (DF in our case)

Answer 16

so sin 60 = 27/3

Answer 17

27/DF :p

Answer 18

sin(60) = sqrt(3)/2 = 27/x

Answer 19

yea but whats DF???

Answer 20

DF is what we have to calculate

Answer 21

so sqrt3/2 gives me df

Answer 22

it helps you get there

\[\frac{\sqrt{3}}{2}=\frac{27}{DF}\]

Answer 23

\[sin(60)=\frac{\sqrt{3}}{2}\]\[sin(60)=\frac{27}{DF}\]
equals are equal, therefore
\[\frac{\sqrt{3}}{2}=\frac{27}{DF}\]

Answer 24

ive noticed the latex codes a little differently lately; some things aint parsing correctly and come out as boxes

Answer 25

for example \[\overbrace x\]

Answer 26

well 0.86 is sqrt 3/2

Answer 27

your options have sqrts in them, so i wouldnt try to approximate it; unless you are going to compare it with approximations of the choices :)

Answer 28

oh ok

Answer 29

do you remember how to cross multiply to solve for the proportion?

Answer 30

\[\frac{a}{b}=\frac{c}{d}\to\ ad=cb\to\ d=\frac{cb}{a}\]

Answer 31

nooo its beeen forever since i have

Answer 32

its a pretty simple, and basic, mathing operation that is sure to awe and amaze your family and friends ;)

Answer 33

well cb would be 54 and ad would be sqrt 3

Answer 34

the answer is 18 sqrt 3 right ?????????

Answer 35

yup

Answer 36

yesss