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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.
To find the ratios for sin X and cos X, we need to determine the length of the opposite and adjacent sides in the right triangle XYZ.
Given:
XY = 12
XZ = 5
YZ = √119
Let's label angle X as θ.
Using the Pythagorean theorem, we can calculate the length of the opposite side (YZ):
YZ^2 = XY^2 - XZ^2
YZ^2 = 12^2 - 5^2
YZ^2 = 144 - 25
YZ^2 = 119
Taking the square root of both sides:
YZ = √119
Now, the opposite side is YZ, the adjacent side is XZ, and the hypotenuse is XY.
sin θ = opposite/hypotenuse = YZ/XY
cos θ = adjacent/hypotenuse = XZ/XY
Plugging in the values:
sin X = √119 / 12
cos X = 5 / 12