## anonymous 4 years ago Given quadrilateral ABCD with AB = 47, BC = 31, CD = 61, angle B = 117 deg and angle C = 76 deg. FIND: 1. AD 2. angle A 3. angle D 4. AC 5. BD NEED YOUR HELP PLEASE! GONNA PASS THIS TOMORROW! THANKYOU!

1. ajprincess

Have u got a diagram for this @ienarancillo?

2. anonymous

3. anonymous

last one please. @ajprincess In the figure, DB =16, angle BAD = 13 deg and angle ABD = 22 deg. Solve for CD. THANKYOU!

4. anonymous

5. Callisto

Are you posting two questions here?

6. anonymous

yes sir. :)

7. Callisto

Not sir :S I'm not a guy. Please do not post two questions in a single post! For the first question, since the diagram is not given, we need to draw one ourselves. |dw:1350743930628:dw| Step 1: find BD, can you?

8. anonymous

OMG! sorry! i didn't mean to! :'(

9. Callisto

It's okay :) Can you find BD?

10. Callisto

By considering triangle BCD.

11. anonymous

i'm going to try solving it now. :)

12. Callisto

Tell me if you need some hints or so.

13. anonymous

can i have a hint please. i am very confused in finding the angles which are along the transversal lines. :(

14. Callisto

Use cosine law. a^2 = b^2 + c^2 - 2bc cosA

15. anonymous

awww. thanks.

16. Callisto

Can you find BD now?

17. anonymous

so.. i drew a separate triangle for this.

18. anonymous

$\sqrt{76^{2}+31^{2}-2(76)(31)\cos(76)}$ = 69.7 BD = 69.7

19. anonymous

sorry it took so long. :"(

20. anonymous

21. Callisto

Is CD = 6 or 76??

22. anonymous

CD = 61 :)

23. Callisto

You typed CD = 6 :S Anyway. No, it's not correct though :|

24. anonymous

OMG! so sorry again! :(

25. anonymous

then what should i do next? :)

26. anonymous

how should i find the angles? :)

27. Callisto

You have to find BD first, and the BD you found is not right. Plug in 61 instead of 76

28. anonymous

oh. sorry. is it 61.4? @Callisto

29. Callisto

Yup. Next step: Find angle CBD

30. anonymous

i used sine law for this. $\frac{ \sin 76 }{ 61.4 } \frac{ \sin \angle CBD }{ 61 } = 74.6 degrees$

31. anonymous

@Callisto is this it? :)

32. Callisto

Yup. So, now, find angle ABD.

33. anonymous

11- 61.4 = 42.4 :)

34. anonymous

i menat 117 - 61.4 = 42.4

35. anonymous

*meant

36. anonymous

@Callisto what should i do next? thanks so much for ur help.

37. Callisto

Next?! Find AD :D By considering triangle ABD.

38. anonymous

sorry. honestly, i ought to do the same thing. :D

39. Callisto

Hmmm you mean?

40. anonymous

uhmm, i was solving it before you replied. i asked you just to be sure. :D is this correct? :) @Callisto

41. Callisto

Wait. It should be 117 - 74.6 = 42.4 And the answer you've got is wrong..

42. anonymous

OMG. so sorry again, i just typed it wrong. but i guess, 42.4 is right? :)

43. Callisto

Yes.

44. anonymous

and is my AD correct? :)

45. Callisto

I think so :|

46. anonymous

sorry. i'll sum up all the remaining 3 answers. im sorry to bother you. but im in the process of understanding it now. :)

47. Callisto

It's okay :) Glad that you're understanding it now :)

48. anonymous

49. anonymous

@Callisto :D

50. Callisto

51. Callisto

It's close to 41.8, but not 41.8

52. anonymous

carelessness of mine. it's 41.4? :O

53. Callisto

Yes!

54. anonymous

but it's math error when i'm solving for angle a.

55. Callisto

It should be sin A/ BD = sin angleABD / AD

56. anonymous

yes. i did that. $\frac{ \sin \angle A }{ 61.4 }\frac{ \sin 42.4 }{ 41.4 } = MATH ERROR$

57. Callisto

Hmm.. can you round your answer above to 4 d.p.? That way, you can get the answer!

58. anonymous

uhmm, our instruction says 'all answers must be rounded off to the tenths place'. :'(