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

 

 Jul 23, 2022
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sin A = 3/4  = BD / BA

 

3/4 = BD / 24

 

(3/4)(24) = BD = 18

 

sin C =  1/4  =  BD / BC

 

4BD = BC

 

4 (18) =  BC = 72

 

DC =  sqrt [ 72^2  - 18^2 ]  =  sqrt  [ 18^2 ( 4^2  - 1^2) ] =  18 sqrt (15)

 

 

 

cool cool cool

 Jul 23, 2022

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