Quadrilaterals and the like

[YoshiRules295]

A field is in the shape of a Quadrilateral...
How do I find these:

a. Find DC distance (meters)
b. Find angles of D and C
c. Find area of the quad

angles are A= 135 degrees, B= 120 degrees
distances are DA= 20 m, AB= 27 m, BC= 24 m

I don't understand how to do this...HELP!!!
:?

 

[stapel]

Since we are given no information about the quadrilateral, nor about how points C and D and the angles C and D (same names for angles and points? confusing!) might relate to it, I see no way to proceed. Sorry.

Eliz.

 

[YoshiRules295]

That explains why I'm confused.

Here's a link to the image:

. . .graphic: 2048-by-1536 pixels, 335 K filesize

Thank you.
_____________________
Edited by stapel -- Reason for edit: Making post viewable

 

[stapel]

Tutors: The complete exercise appears to be as follows:

Let ABCD be a quadrilateral, with CD the "base", and DA and BC being, respectively, the left and right sides. |AB| = 27 meters, |BC| = 24 m, and |DA| = 20 m; the length of |CD| is not given. Use "m(theta)" to mean "the measure of angle theta", we have m(DAB) = 135° and m(ABC) = 120°; the other two angle measures are not given.

From this information, find the length of side CD, find the measures of the angles BCD and CDA, and find the area of the quadrilateral.

    A     27     B
     *----------*
    / 135°   120° \
20 /               \ 24
  /                 \
 *-------------------* 
D                     C

But AB and CD do not appear parallel in the graphic.

YoshiRules295: For future reference, it is usually better to use smaller images, both because they transfer more quickly and because they can be viewed without a lot of scrolling.

Meanwhile, with respect to this exercise: What formulas do you have? What have you tried? How far have you gotten?

Thank you.

Eliz.

 

[YoshiRules295]

I think I got it!!!
You have to use Law of Cosines!!!

Yea for me!!!

 

[YoshiRules295]

i've tried law of cosines for the first and got DC= square root of (100cosC)

 

[YoshiRules295]

I can't figure out angle C. I've tried law of cosines.
Now i'm trying law of sines.

 

[YoshiRules295]

law of sines doesn't work, either.

 

[stapel]

The Law of Sines and the Law of Cosines apply to triangles, don't they...? How are you using them for this quadrilateral?

Please reply showing your work. (We can't help you find errors if we can't see what you've done.)

Thank you.

Eliz.

 

[Denis]

Join AC: you now have triangle ABC with angleB = 120, AB = 27, BC = 24:
ABC is eagerly awaiting you to apply Law of Cosines!

Join BD: you now have triangle ABD with angleA = 135, AB = 27, AD = 20:
ABD is eagerly awaiting you to apply Law of Cosines!