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Write the ratios for sin X
and cos X
.
Right triangle XYZ with right angle Z is shown. XY is labeled 12. XZ is labeled 5. YZ is labeled start root 119 end root.
(2 points)
To find sin X and cos X, we first need to find the length of the side opposite angle X and the length of the side adjacent to angle X.
Using the Pythagorean theorem:
XY^2 + XZ^2 = YZ^2
12^2 + 5^2 = 119
144 + 25 = 169
√169 = 13
So, the length of side YZ is 13.
Now, we can find sin X and cos X:
sin X = opposite/hypotenuse = YZ/XY = 13/12
cos X = adjacent/hypotenuse = XZ/XY = 5/12
Therefore, the ratios for sin X and cos X in this triangle are:
sin X = 13/12
cos X = 5/12