Right-Triangle Trig

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

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 :-)