Question

In △DEF, what is the length of DF ?

90

45√2

15√3

30√3

Answer 1

Use sine ratio to find DF
\[sin60 = \frac{45}{DF}\]

Answer 2

(45)sin60 = 38.97114317

Answer 3

Not really.

Answer 4

so then???

Answer 5

Multiply both sides by DF. Then divide both sides by sin60. What do you get?

Answer 6

I dont know what DF equals

Answer 7

ok... Sin 60 = 45/ DF

Therefore DF = 45/ sin 60 = 45/\[\sqrt{3}/2\] = 90/ sq rt 3...

Answer 8

oh, ok. So 51.96

Answer 9

so, 30 sqrt 3

Answer 10

yup.. 51.96.. if u simplify further...

Answer 11

Hmm You'll now what DF equal to
\[sin60=\frac{45}{DF}\]Multiply both sides by DF.
\[DFsin60=DF(\frac{45}{DF})\]\[DFsin60=45\]
Then divide both sides by sin60.
\[\frac{DFsin60}{sin60}=\frac{45}{sin60}\]\[DF=\frac{45}{sin60}=...\]

Answer 12

Thank you both :)

Answer 13

\[\frac{45}{sin60} = \frac{45}{\frac{\sqrt3}{2}} = \frac{90}{\sqrt3} = \frac{90\sqrt3}{3} = 30\sqrt3\]

Answer 14

perfect.. multiply and divide by root 3.. denominator comes to be 3.. divide 90 by it..

So 30 rt 3...