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Expert: - 9/18/2009


Question
hi sir

please help me. my qeustion is this- in quadrilateral ABCD, AB is 2 units long, BC is 4 units long, CD is 4 units long, and AD is 5 units long. The angle A and C are congruent. whats the length of diagnol BD.


Answer

Quad
Questioner: marcus
Country: United States
Category: Advanced Math
Private: Yes
Subject: geometry
Question: hi sir

please help me. my qeustion is this- in quadrilateral ABCD, AB is 2 units long, BC is 4 units long, CD is 4 units long, and AD is 5 units long. The angle A and C are congruent. whats the length of diagnol BD.
.................................................................

Looks like law of cosines:

x^2 = 4 + 25 - 20 cos A

x^2 = 16 + 16 - 32 cos A

Solve simultaneous equations:

4 + 25 - 20 cos A = = 16 + 16 - 32 cos A

29 - 20 cos A = = 32 - 32 cos A

12 cos A = 3

cos A = 1/4

Now you can go back and find x.

Paul Klarreich

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I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

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