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In quadrilateral BCED, we have BD = 11, BC = 9, and CE=2. Sides BD andCE are extended past B and C, respectively, to meet at point A. If AC = 28 and AB = 24, then what is DE?

 Jun 6, 2020
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In triangle(ABC), you have:  AB = 24,  AC = 28.  and  BC = 9.

Since you have the three sides, use the Law of Cosines to find angle(A)

  a2  =  b2 + c2 - 2·b·c·cos(A)

  92  =  282 + 242 - 2·28·24·cos(A)

Solve this for angle(A).

 

Now, look at triangle(ADE).

AD = 35, AE = 30, and you have angle(A) from above.

Use the Law of Cosines for this triangle.

  a2  =  b2 + c2 - 2·b·c·cos(A)

  a2  =  352 + 302 - 2·35·30·cos(A)

 Jun 6, 2020

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