Write the ratios for sin X

Question

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.

Answer 1

To find the ratios of sine and cosine:

Sine (sin) of angle X is equal to the length of the side opposite angle X (YZ) divided by the length of the hypotenuse (XY):

sin(X) = YZ / XY

Given that YZ is √119 and XY is 12:

sin(X) = (√119) / 12

Cosine (cos) of angle X is equal to the length of the side adjacent to angle X (XZ) divided by the length of the hypotenuse (XY):

cos(X) = XZ / XY

Given that XZ is 5 and XY is 12:

cos(X) = 5 / 12

Therefore, the ratios for sin X and cos X are:

sin(X) = (√119) / 12
cos(X) = 5 / 12