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In right triangle $XYZ$, shown below, what is $\sin{X}$?

 

 Jul 6, 2018
 #1
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Cos(X) = Cos(8/10) =0.8

Arccos(0.8) = X = 36.87 degrees.

Sin(X) = Sin(36.87) =6/10 - This is accurate because:

10^2 =8^2 + 6^2

 Jul 6, 2018
 #2
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It is a Pythagorean triple. The length of YZ is 6, as 102-82=62

 

As we are concerned with the angle at X, the hypotenuse is the side XZ and the opposite is the side YZ.

 

Using SOHCAHTOA, we know that sinx=O/H, meaning that sinx=6/10

 

Therefore our answer is 6/10 or 0.6 :-)

 Jul 8, 2018

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