The problem is: Given parallelogram ABCD with diagonals <mover> <mi mathvariant="no

anginih86

anginih86

Answered question

2022-06-24

The problem is: Given parallelogram ABCD with diagonals A C ¯ and B D ¯ intersecting at E. If m   A E B=60 degrees, m   C A B=30 degrees, and AB=18, find AD.
This problem seems simple, and I presume that you use the properties of special right triangles; however, I can't seem to get the right answer. The answer is 6   21. Thank you!

Answer & Explanation

Amy Daniels

Amy Daniels

Beginner2022-06-25Added 20 answers

Since A B E = 90 , we obtain
B E = 18 tan 30 = 6 3 ,
which gives
B D = 12 3 .
Thus,
A D = 18 2 + ( 12 3 ) 2 = 756 = 6 21 .

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