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In the diagram below, we have AD = 24 and ADB = 90 degrees. If sin A = 2/3 and sin C = 1/4, then what is DC?

 

 May 5, 2022
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sin A = 2/3  

 

So tan   A =   2 / [ 3^2 - 2^2 ] =  2 / sqrt 5

 

So 

 

tan A =   2/sqrt 5

BD /AD  =  2/sqrt 5

BD / 24 = 2/sqrt 5

BD =  48/sqrt  5  

 

sin C  =1/4

tan C  =    1 / [ 4^2 - 1^2 ]  =  1/ sqrt 15

 

So

tan C = 1/sqrt 15

BD / DC =  1/sqrt 15

(48 /sqrt 5)  / DC  =  1/sqrt 15

 

So

DC  =  (48/sqrt 5) / (1/sqrt 15)

DC =   48 (sqrt 15 / sqrt 5 )

DC  =  48sqrt 3

 

cool cool cool

 May 5, 2022

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