## Emily778 2 years ago Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

1. Emily778

|dw:1362774575688:dw|

2. jim_thompson5910

is that a 9? or a 4?

3. Emily778

9

4. jim_thompson5910

ok thanks

5. jim_thompson5910

here's the template again |dw:1362774782473:dw| I would add this to your notes if you don't have it already

6. jim_thompson5910

notice how the number in front of the sqrt(3) on the longer leg is 9 so that must mean that x = 9

7. Emily778

how did you get 30 and 2x?

8. jim_thompson5910

well the given angle is 60, which adds to the right angle 90 to get 90+60 = 150 the remaining angle must be 30 in order for the three to add to 180

9. jim_thompson5910

since 150 + 30 = 180

10. jim_thompson5910

as for the 2x... the hypotenuse is always twice as long as the shorter leg in a 30-60-90 triangle

11. jim_thompson5910

so that explains the x for the shorter leg and 2x for the hypotenuse

12. Emily778

should I write that process down?

13. jim_thompson5910

yes I would if you're not familiar with it

14. Emily778

would it be a good idea to write it on my homework?

15. jim_thompson5910

if you want to, there's nothing wrong with using this template

16. jim_thompson5910

you can draw the template off to the side and show that x must be 9

17. jim_thompson5910

when you match up the terms

18. Emily778

why did you get rid of the 9?

19. jim_thompson5910

what do you mean?

20. Emily778

it was 9 sqrt 3? now, it's X sqrt 3?

21. jim_thompson5910

no, I said x was 9 so x = 9

22. jim_thompson5910

oh i see what you mean

23. Emily778

you said in the picture above..

24. jim_thompson5910

9 * sqrt(3) ... what we're given x * sqrt(3)... template

25. jim_thompson5910

notice how the x and the 9 match up

26. Emily778

oh.

27. jim_thompson5910

so that's how I got that x = 9

28. jim_thompson5910

the y and the 2x match up, so y = 2x y = 2*9 y = 18

29. Emily778

you are so confusing me. Can you write it out like, step 1, step 2. And start from the beginning cause I'm lost

30. jim_thompson5910

did you see how I got x = 9?

31. jim_thompson5910

here is your triangle (on top) and the general template triangle (on bottom) |dw:1362776258556:dw|

32. jim_thompson5910

notice how these two sides match up |dw:1362776369974:dw|

33. Emily778

can we not use the template? it's confusing

34. jim_thompson5910

have you learned trig yet?

35. Emily778

can you just show me the process of how to solve this?

36. jim_thompson5910

I'm just curious because if you have, then we can use that

37. Emily778

I just wanna solve it..

38. jim_thompson5910

I know, but I need to know if you know trig so it will make sense if I use it

39. jim_thompson5910

have you learned things like sine, cosine, tangent, etc?

40. Emily778

I think

41. jim_thompson5910

so you've seen things like sine = opposite/hypotenuse ?

42. jim_thompson5910

I'll assume yes

43. jim_thompson5910

tan(30) = opposite/adjacent tan(30) = x/(9*sqrt(3)) sqrt(3)/3 = x/(9*sqrt(3)) ... use a calculator or the unit circle here sqrt(3)*9*sqrt(3) = 3x 9*sqrt(3)*sqrt(3) = 3x 9*3 = 3x 27 = 3x 3x = 27 x = 27/3 x = 9 so you can see that we get the same answer as we did before

44. jim_thompson5910

sure this method is a bit more complicated, but it works it all hinges on whether you know trig or not

45. Emily778

do I write that down?

46. jim_thompson5910

yeah, or you could skip a few steps I guess

47. jim_thompson5910

wherever you see a 'sqrt', use the square root symbol of course

48. Emily778

Should I write this down and skip all the other steps? :) sqrt(3)*9*sqrt(3) = 3x 9*sqrt(3)*sqrt(3) = 3x 9*3 = 3x 27 = 3x 3x = 27 x = 27/3 x = 9

49. jim_thompson5910

I would have the previous steps in there, these ones tan(30) = opposite/adjacent tan(30) = x/(9*sqrt(3)) sqrt(3)/3 = x/(9*sqrt(3)) ------------------------------------------------------- I guess you could skip step 2 to get just these steps tan(30) = opposite/adjacent sqrt(3)/3 = x/(9*sqrt(3))

50. Emily778

I'm confused. Is this 3 times 9? sqrt(3)*9*sqrt(3) = 3x

51. jim_thompson5910

yeah it's just a complicated way of saying 9*3

52. Emily778

so it's actually 9 times 3 sqrt 3= 3x

53. jim_thompson5910

no the sqrt(3) terms multiply to 3 so that's why 9*sqrt(3)*sqrt(3) = 3x turns into 9*3 = 3x

54. Emily778

I got the x. What's the Y?

55. Emily778

@jim_thompson5910

56. jim_thompson5910

well y = 2x so y = 2*9 = 18

57. jim_thompson5910

so y = 18

58. jim_thompson5910

you can use the pythagorean theorem to confirm, but you'd get the same answer (just in a more complicated way)

59. Emily778

how did you find that Y= 2x?

60. jim_thompson5910

well you would use the template...but just remembered you don't like that template very much

61. jim_thompson5910

so you can use a^2 + b^2 = c^2 to find the value of y

62. jim_thompson5910

a^2 + b^2 = c^2 9^2 + (9*sqrt(3))^2 = y^2 81 + 243 = y^2 keep going to solve for y

63. Emily778

y=18?

64. jim_thompson5910

yes good

65. Emily778

okay, 2nd problem! :p

66. Emily778

Recreation. A skateboarding ramp is 12 inches high and rises at an angle of 17 degrees. How long is the base of the ramp? Round to the nearest inch.

67. Emily778

@jim_thompson5910

68. jim_thompson5910

|dw:1362781717017:dw|

69. jim_thompson5910

tan(17) = 12/x x*tan(17) = 12 x = 12/tan(17) x = ???

70. Emily778

do you not know X?

71. Emily778

@jim_thompson5910

72. jim_thompson5910

not until you solve for it

73. jim_thompson5910

by typing 12/tan(17) into the calculator

74. Emily778

oh lol

75. jim_thompson5910

yeah it's not too bad to find

76. Emily778

39.25

77. jim_thompson5910

yep

78. Emily778

79. jim_thompson5910

yes it is

80. Emily778

Last question. I was wrong btw. There's only 3 questions left, not 4. :P

81. jim_thompson5910

ok works for us lol

82. Emily778

The lengths of the diagonals of a rhombus are in 2 inches and 5 inches. Find the measures of the angles of the rhombus to the nearest degree.

83. jim_thompson5910

|dw:1362782836744:dw|

84. jim_thompson5910

|dw:1362782951298:dw|

85. jim_thompson5910

we get this triangle |dw:1362782979724:dw|

86. jim_thompson5910

let x and y be the two unknown angles |dw:1362783041003:dw|

87. jim_thompson5910

tan(x) = 1/2.5 tan(x) = 0.4 x = arctan(0.4) x = ??

88. Emily778

do I draw all of these?

89. jim_thompson5910

you don't have to, but it helps to see how to get the answer

90. Emily778

okay

91. jim_thompson5910

so what do you get for x?

92. Emily778

wait, what's arctan?

93. jim_thompson5910

it's the inverse of tangent

94. jim_thompson5910

if you don't have a calculator that can handle arctan, then look here http://www.google.com/search?hl=&q=arctan%280.4%29+in+degrees&sourceid=navclient-ff&rlz=1B3GGLL_enUS420US420&ie=UTF-8

95. Emily778

how do I get it on my calculator?

96. jim_thompson5910

at the top, you'll see that " arctan(0.4) = 21.8014095 degrees"

97. jim_thompson5910

if you have a TI-83, 85, 86, etc you can hit 2nd, then tan to get arctan

98. Emily778

where's arc on the calculator?

99. jim_thompson5910

what kind of calculator do you have?

100. Emily778

it said "Atan" when i did that, not arctan

101. Emily778

But I still got the right answer

102. jim_thompson5910

oh same thing

103. jim_thompson5910

atan is just a shorter version of arctan

104. Emily778

thankyou. :-)

105. jim_thompson5910

np what did you get for x?

106. Emily778

21.8

107. Emily778

btw, do I find Y?

108. jim_thompson5910

y = 90 - x y = 90 - 21.8 y = 68.2

109. jim_thompson5910

now that you know x and y, you would double them to find the angles of the rhombus

110. jim_thompson5910

21.8*2 = 43.6 which is the measure of one set of angles of the rhombus 68.2*2 = 136.4 which is the measure of another set of angles of the rhombus

111. Emily778

112. jim_thompson5910

what do you mean

113. Emily778

oh..double them seperately.

114. jim_thompson5910

yes

115. jim_thompson5910

because we want the angles of the rhombus, not the triangle

116. Emily778

okay, what do I do after?

117. jim_thompson5910

you're done, you found the angles of the rhombus

118. Emily778

oh, so x= 43.6 and y=136.4?

119. jim_thompson5910

no those are the two angles of a rhombus

120. jim_thompson5910

the other two are congruent to those two

121. jim_thompson5910

we have something like this |dw:1362784125897:dw|

122. Emily778

should I draw that?

123. jim_thompson5910

the diagonals are 5 and 2, I just didn't have enough room to draw them in

124. jim_thompson5910

no, they just want the angles

125. jim_thompson5910

you can if you want

126. Emily778

where are the diagonals?

127. jim_thompson5910

lol like i said, i didn't have enough room

128. jim_thompson5910

|dw:1362784257953:dw| see how things get cut off?

129. Emily778

yeah

130. Emily778

so, I'm done now?

131. jim_thompson5910

yes pretty much

132. Emily778

:D YAYAYAYAYAY

133. jim_thompson5910

lol