Question

Pic.
In △DEF, what is the length of line segment DF?

A: 126
B: 63 radical 2
C: 21 radical 3
D: 42 radical 3

Answer 1

Not that the angle between DF and ED is 180-90-60=30

Hence cosine projection would imply the length DF satisfies;

63=DFcos(30)

Rearrange for DF yields;

DF = 63/(cos(30))
=> DF = 42*sqrt(3)

i.e. answer D.

Answer 2

Is there any way you can explain that in another way?

Answer 3

Do you know the trigonometric relations known as

SOH CAH TOA?

Answer 4

Yeah kind of

Answer 5

Well, in that case, another way to go about it would be to note that your

Hypotenuse, H is the side FD (the side you are looking for)

the Opposite side, O is the side ED, which you have as 63

and the angle theta is 60deg.

Using the trig. relation SOH (as these include the variable you have & require)

this implies that;

Opposite = Hypotenuse * Sin(theta)

which in this case you can rearrange for the Hypotenuse (which you want);

H = O/(Sin(theta))

So H = FD = 63/(sin(60) = 42*sqrt(3)

Answer 6

Woah, well that made a bit about more clear for me, still about confusing, but this is much appreciated ya'll. thank you so much,

Answer 7

Can ya'll help me with one more?
& thanks(:

Answer 8

Sure, why not

Answer 9

For the left hand side of the picture, you require the hypotenuse, and you are given the adjacent side (and the angle). For the right hand side you also require the hypotenuse and you are given the adjacent (and angle).

Hence for both you need to use the trig. relation

CAH, which implies;

Adjacent = Hypotenuse*cos(angle)

For both sides, this means that the hypotenuse satisfies;

H = A/(cos(angle)

For the left side, this is;

H = 64/cos(45) = 90.5cm

and for the right side;

H = 106/cos(30) = 122.4cm

Both to the nearest 1 decimal place.

Answer 10

I have a feeling I am going to struggle with this stuff for a little while. But when you lay it out like that, makes more sense.

Answer 11

& thanks!!! :D

Answer 12

No problem