## anonymous one year ago Hi, this is my moms account I need help with a question I will fan and do a testimonial and best response if you help

1. anonymous

In triangle DEF measurement angle D=45 degrees meausrement angle E=63 degrees and EF= 24 inches. What is DE to the nearest tenth of a inch

2. anonymous

there isnt a drawing

3. Astrophysics

|dw:1433827926366:dw| Hey so I think we can make a triangle as such, so we have an idea what we're looking for :)

4. anonymous

Okay so we are looking for x

5. Astrophysics

Yes, I just put a big question mark there instead so we know :), ok lets find the third angle first, and this seems like a sine law problem, so can you first tell me how many degrees are in a triangle?

6. anonymous

90

7. Astrophysics

Not quite, you may be thinking of a right triangle which is 90 degrees, but all triangles add up to 180, so our equation for the third angle would be as follow $45 + 63 + x = 180$

8. anonymous

oh im sorry...so i would add 45 and 63 then subtract from 180?

9. Astrophysics

So just for convenience our third angle will be 72 degrees |dw:1433828380399:dw| ok so we have to use the sine law here, which can be used in any triangle where we have a side and its opposite angles, and yes!

10. anonymous

whats next?

11. Astrophysics

|dw:1433828458402:dw| $\frac{ a }{ \sin(A) } = \frac{ b }{ \sin(B) }$ where A and B are known angles.

12. Astrophysics

Or we can use |dw:1433828607515:dw|

13. Astrophysics

$\frac{ x }{ \sin(72) } = \frac{ 24 }{ \sin(63) }$ please check my work :)

14. anonymous

okay I get it so far

15. anonymous

why is it 72 and not 45?

16. Astrophysics

Now you just do the algebra for x, and we should get x!

17. anonymous

cross multiply...72 times 24 =63x?

18. Astrophysics

Because we need to find the length of a side, so we use the formula to find length on top, and we know the sin theta ratio.

19. Astrophysics

Yup, cross multiply works :) $x \times \sin(63) = 24 \times \sin(72)$

20. anonymous

sin 72 is .25382

21. anonymous

multiply that by 24?

22. Astrophysics

Yes

23. anonymous

6.0971

24. Astrophysics

Mhm, that does not look right

25. Astrophysics

sin(72) I got 0.95105...

26. Astrophysics

Make sure you're in degree mode on your calculator

27. Astrophysics

We should approximately get a length close to 24 (bit higher)

28. Astrophysics

for the final answer that is

29. anonymous

okay hold on

30. Astrophysics

31. anonymous

22.825?

32. anonymous

@wolf1728 can you finish off?

33. Astrophysics

Ok now find x

34. anonymous

divide by sin 63?

35. Astrophysics

Good!

36. anonymous

I got .039

37. anonymous

my choices are 30.2 15.1 32.3 10.5

38. anonymous

I have to go soon and I have more questions to ask for tomorrow

39. wolf1728

I'm looking for the answers so far The angles are 45 63 and 72 and 1 side = 24

40. anonymous

correct thats what @Astrophysics and I got to

41. wolf1728

I calculate the other 2 sides as 19.047 and 25.617

42. Astrophysics

Yes, I got the same

43. Astrophysics

Maybe I made an error in the ratios, mhm...

44. wolf1728

Okay, then we're all set

45. anonymous

what is DE though?

46. anonymous

thats not an answer choice though

47. Astrophysics

Try 30.2

48. wolf1728

DE = 25.617 So, are the ONLY answers we can agree on are angles are 45 63 and 72 and 1 side = 24

49. anonymous

why 30.2?

50. anonymous

yes because 25 isnt a choice

51. Astrophysics

Yes, I'm getting the same answer, how many attempts do you have?

52. anonymous

just 1

53. anonymous

and 2 more kinda like it

54. wolf1728

I redrew the figure

55. anonymous

56. Astrophysics

Yes, that will work out much better!

57. wolf1728

Okay here's the NEW redrawn figure

58. anonymous

okay now how do we use it to solve the problem

59. Astrophysics

So side a = 24, b = 32.2, and c = 30.24

60. Astrophysics

So 30.2 sounds about right, what do you think wolf?

61. anonymous

how did you get c=30.24?

62. anonymous

Im sorry im asking so much

63. wolf1728

I think the MAIN problem is interpreting the Law of Sines properly. We should agree on what exactly is angle A angle B angle C and side a side b side c

64. anonymous

alright we know that ef=24

65. Astrophysics

Ok, so lets use the original triangle |dw:1433831084347:dw|

66. anonymous

@wolf1728 do you agree so far?

67. Astrophysics

$\frac{ a }{ \sin(a) } = \frac{ c }{ \sin(c) } \implies \frac{ 24 }{ \sin(45) } = \frac{ x }{ \sin(63) }$ $\implies \frac{ 24 \sin(63) }{ \sin(45) } = x$

68. Astrophysics

Sorry I misread my own triangle earlier haha.

69. anonymous

Oh so what I pointed out was right!

70. anonymous

lol

71. wolf1728

Okay I redrew it in terms of A B and C and sides a ,b and c

72. Astrophysics

Now it should make sense, is that good @Miss.SweetiePie haha :)

73. anonymous

so we multiply sin 63 by 24?

74. Astrophysics

Yes

75. anonymous

.8910 is sin 63 now multiply by 24?

76. wolf1728

Astrophysics, you are stating that a/sin(A) = c/sin (C) we know angle A and angle C but we do NOT know side a or side c

77. Astrophysics

side a = 24

78. wolf1728

I'd say we should be interpreting the Law of Sines PRECISELY or else we'll get incorrect answers.

79. anonymous

So how do we do that

80. Astrophysics

I used my original triangle

81. Astrophysics

Only thing I didn't state was the angles, but those seem to be pretty obvious :P

82. wolf1728

Here is what I have for the Law of Sines:

83. anonymous

I got 30.2 doing it that way

84. Astrophysics

Yes, I got the same

85. anonymous

86. anonymous

@Astrophysics and @wolf1728 can you help with 2 more and then ill give both of you testimonials and fan

87. wolf1728

I'm not sure. If you two agree then I'll say okay.

88. wolf1728

89. anonymous

thank you is it okay if I put it in here

90. Astrophysics

Haha, well this was all over the place, please open a new question @Miss.SweetiePie

91. wolf1728

sure - it's okay (I don;t need another medal)

92. wolf1728

Okay if you want a nice clean space then start a new question.

93. Astrophysics

Haha it's ok we can do it here, hey @Miss.SweetiePie was 30.2 right

94. anonymous

@Astrophysics is it okay to do one morein here then I open a new one?

95. wolf1728

96. anonymous

I'm not sure yet I havent sent it off

97. Astrophysics

I guess we should move on, before I start doubting myself :P

98. anonymous

Okay In triangle XYZ XY=13 YZ=20 and XZ=25 what is the measure of angle Z to the nearest degree

99. anonymous

what whats wrong

100. Astrophysics

Never mind lets ignore it haha

101. Astrophysics

I was just doubting

102. anonymous

lol okay...do you see the problem I just put up and please dont say that

103. wolf1728

I drew the diagram

104. Astrophysics

|dw:1433832486973:dw|

105. Astrophysics

WE CAN USE COSINE LAW

106. Astrophysics

$a^2=b^2+c^2 - 2bc \cos(A)$

107. anonymous

okay so now we jus have to find angle z

108. Astrophysics

I think you should try to apply it now, and we'll just guide you :P, you have to learn this not us!

109. anonymous

13^2=20^2+25^2?

110. wolf1728

That is NOT a right triangle -(I think astrophysics knew that though)

111. Astrophysics

Yes, sorry the drawing should not be a right triangle, a bit more tilted

112. wolf1728

Okay - maybe we ALL knew that LOL

113. anonymous

wait so what do I do? do I still do th 13^2 part

114. Astrophysics

Well first lets specify the angle|dw:1433832804456:dw|

115. anonymous

thats the unknown angle

116. wolf1728

Here is what I have for Cosine Law

117. wolf1728

We know all three sides so I think we have to use one of those formulas

118. anonymous

Cos(C) ?

119. Astrophysics

Yes, that's what we are looking for, that's for a triangle that looks as such |dw:1433832986527:dw| yes cos(C) looks good to me as well

120. anonymous

So a^2 would be j13^2?

121. Astrophysics

|dw:1433833163502:dw|

122. wolf1728

cosine (A) = [b^2 +c^2 - a^2] / (2*b*c) cosine (B) = [a^2 +c^2 - b^2] / (2*a*c) cosine (C) = [a^2 +b^2 - c^2] / (2*a*b)

123. Astrophysics

|dw:1433833225147:dw|

124. Astrophysics

Now that's clear, at this point, we just plug and chug :P

125. anonymous

oh so a would be 25^2 correct?

126. anonymous

b=20^2

127. anonymous

minus 13^2?

128. Astrophysics

Yeah

129. anonymous

so 1025-169=856 but we have to find the sr

130. Astrophysics

sr?

131. Astrophysics

cosine (C) = [a^2 +b^2 - c^2] / (2*a*b)

132. anonymous

which is 29.25

133. anonymous

so so far we have cos*C* 29.3/ 1000?

134. Astrophysics

Not sure what you're doing, I did it all in one step

135. Astrophysics

856 sounds good you need to divide by (2*a*b)

136. Astrophysics

Then we can find angle z

137. anonymous

so 856/1000?

138. Astrophysics

Yes now find the angle

139. Astrophysics

$\cos(c) = .856$ do you know how to find angle c?

140. Astrophysics

You have to take the inverse

141. Astrophysics

$c = \cos^{-1} (0.856)$

142. wolf1728

cosine (C) = [a^2 +b^2 - c^2] / (2*a*b) cosine (C) = [25^2 + 20^2 -13^2] / 2*25*20 cosine (C) = [625 + 400 -169] / 1,000 cosine (C) = 856 / 1,000 cosine (C) = .856 Arc cosine (.856) = 31.13 degrees

143. anonymous

inverse that okay let me calculatw

144. Astrophysics

Haha, right on wolf :)

145. wolf1728

Gee thanks :-)

146. anonymous

147. anonymous

so thats it for that? nothing else?

148. anonymous

Im going to open up another question I have one more I think but can we go slow to make sure im still there

149. anonymous

understanding

150. Astrophysics

Yup, that's it to it :)

151. wolf1728

Need a good trigonometry calculator? Try this http://www.1728.org/trigcalc.htm

152. Astrophysics

The main thing is, you need to know how to set up the triangle

153. wolf1728

Absolutely, Astrophysics

154. anonymous

okay one more then I should be good...let me try to set it up in the enxt question please

155. Astrophysics

156. wolf1728

So, how about those Red Sox? LOL

157. Astrophysics

Haha, I wouldn't be sure, don't follow baseball, but I'm assuming there is a joke in there somewhere!

158. wolf1728

No I just typed something to fill in the space.