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Math Help - thales theorem and similar triangles

  1. #1
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    thales theorem and similar triangles

    could someone explain how you can use thales theorem to find sinA as the question hints?(click on link below) I have solved the larger of the two right triangle for DB. then found C and and B of the same triangle with arctan. i also know by pythagorean theorem that the smaller triangle is a similar right triangle to the larger and D is 90deg. so i use the sine law to find the lenght of AC and AD.

    BUT! the book has not even gone into law of sine and cosine yet. i answered a, b and c. but still have no idea how he wants me to use thales theorem to find siaA? or how to find AC AD without law of sine.

    thales theorem and similar triangles-example.jpg
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  2. #2
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    triangle CDB is a right triangle similar to triangle ADC

    since angle A = angle DCB

    \sin(A) = \sin(\angle DCB) = \frac{\sqrt{13}}{4}

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  3. #3
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    ah i see the easy way. thanks. but i don't think you need old boy thale for this? except i guess to prove that DCB triangle is a right triangle? as i understand it thales theorm is to show that you have a right triangle in the circle from 2 isosceles triangles. maybe i miss something.
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  4. #4
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    Thale's theorem only says DCB is a right triangle ... I guess you actually needed it to establish the similarity between triangles CDB , ADC, and ACB
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