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In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$.  If $\sin A = \frac13$ and $\sin C = \frac12$, then what is $BC$?

 

 Jun 1, 2024
 #1
avatar+129487 
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sinA =  1/3

So

BD / AB  =  1/3

BD / 24  = 1/3

BD = 24 (1/3)  = 8

 

 

sin C = 1/2

Angle C  = arcsin (1/2)  = 30°

Then triangle BDC  is a 30-60-90  right triangle

 

BD  = 8

So  BC   =  2BD  = 2 * 8  =   16

 

cool cool cool

 Jun 1, 2024

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