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Precalculus Question Using Trig to Find Side Length

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In quadrilateral ABCD, we have ∠A = ∠C = 90◦ , ∠BDA = 2∠BDC, AB = 6, and AD = 8. Find the length of BC. (Diagram Below)

 

 Dec 2, 2020

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 #1
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Hint: From Pythagorean Theorem, BD=10. Proceed to find the value of angle BDA from Law of Cosines (or Law of Sines, if you like that better) which gives you angle BDC. Then you have all of the angles in triangle BDC and one side, so use Law of Cosines to find BC.

 Dec 2, 2020
 #2
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Is there a way to solve this without using a calculator? I know that with the Law of Cosines I have to do the arccos to get the angle, but that requires a calculator (at least for arccos(4/5)) and I want to try and solve it without using one.

Guest Dec 2, 2020
 #3
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In quadrilateral ABCD, we have ∠A = ∠C = 90◦ , ∠BDA = 2∠BDC, AB = 6, and AD = 8. Find the length of BC.

 Dec 2, 2020

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