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enter image description hereIn an isosceles triangle ABC, side AB and AC are equal in length. There exists a point D on the side AB. The angle BAC is theeta . The side AD is two units smaller than AC .What is the generalized formula to calculate the side CD.

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I have tried this thing. I think that the formula would require some simple trignometry. –  Vinay - mathematician. May 28 at 15:38
    
BD can be anything. –  mercio May 28 at 15:41
    
yes bd can be anything. –  Vinay - mathematician. May 28 at 15:50
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Use the Law of Cosines –  Graham Kemp May 28 at 16:01
    
I am asking for a proof in an algebraic form. Well I have also applied the law of cosines –  Vinay - mathematician. May 28 at 16:02

2 Answers 2

This is a simple application of the cosine rule to the triangle $ACD$

$$CD^2=(a-2)^2+a^2-2a(a-2)\cos\theta$$

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Ok I will verify and confirm it. –  Vinay - mathematician. May 29 at 14:48
    
ok thank you this works. good job –  Vinay - mathematician. May 29 at 15:02

You can draw a picture to convince yourself that the length of $BD$ does not depend on $\theta$. You will need to be given more information.

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