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In \(\triangle{RST}\), shown, \(\sin{R}=\frac{2}{5}\). What is \(\sin{T}\)?

 Jun 28, 2019
 #1
avatar+8965 
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sin( angle )  =  opposite / hypotenuse

 

sin( R )  =  TS / 5

 

2 / 5  =  TS / 5

 

2  =  TS

 

Now we can find the length of RS using the Pythagorean Theorem.

 

22 + RS2  =  52

 

RS2  =  52 - 22

 

RS2  =  21

 

RS  =  √[ 21 ]

 

sin( angle )  =  opposite / hypotenuse

 

sin( T )  =  RS / 5

 

sin( T )  =  √[ 21 ] / 5

 Jun 28, 2019

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