ASAPT
  • ASAPT
Find the value of x and the value of y.
Mathematics
jamiebookeater
  • jamiebookeater
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ASAPT
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ASAPT
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im not sure im pretty bad at geometry
ASAPT
  • ASAPT
ok do you know the answer?

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anonymous
  • anonymous
You can't use the law of cosines unless you know the angle opposite the side you're looking for.
ASAPT
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oh ok do you know the answer?
ASAPT
  • ASAPT
ugh why is this so difficult
ybarrap
  • ybarrap
Look at the lengths of CB and BA. What is their sum?
ybarrap
  • ybarrap
Compare this sum to 48. How is this possible?
ybarrap
  • ybarrap
There is only one explanation. Once you see this, the answer will POP.
ybarrap
  • ybarrap
Actually, just look at the lengths of CE and BA.
ybarrap
  • ybarrap
Sum them and compare to 48. What MUST x be in this case?
ASAPT
  • ASAPT
48?
ybarrap
  • ybarrap
You know that the lengths of 2 sides of a triangle MUST be greater than the third side, right?
ASAPT
  • ASAPT
yea
ASAPT
  • ASAPT
so what would that mean my answer is @ybarrap
ybarrap
  • ybarrap
forget about that approach
ASAPT
  • ASAPT
ok
ASAPT
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its 12 12
ybarrap
  • ybarrap
this can't be right, forget that approach too. The reason is that y could be anything and that doesn't make sense.
ASAPT
  • ASAPT
no it was I submitted it and it said it was right
ASAPT
  • ASAPT
I have more to do if you want to help
anonymous
  • anonymous
|dw:1436331441040:dw|
ybarrap
  • ybarrap
I just realized angle D and angle B are equal :( @surjithayer used similarity - Nice job!
mathstudent55
  • mathstudent55
You are dealing with two similar triangles. Since
mathstudent55
  • mathstudent55
Now we see how the triangles are similar. Since x is part of side BC, we need the length of side BC. From similarity, we get this proportion: \(\dfrac{CE}{CA} = \dfrac{CD}{BC} \) \(\dfrac{24}{48} = \dfrac{18}{BC} \) \(\dfrac{1}{2} = \dfrac{18}{BC} \) \(BC = 36\) Since \(BC = 36\), and \(CE = 24\), then \(x = BE = 36 - 24 = 12\) Now we need y. \(\dfrac{CE}{CA} = \dfrac{DE}{BA} \) \(\dfrac{24}{48} = \dfrac{y}{24} \) \(\dfrac{1}{2} = \dfrac{y}{24} \) \(y = 12\)

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