Question

Find the values of the variables if necessary round your answers to the nearest tenth

Answer 1

B. x=8.2, y=21.5

Step-by-step explanation:

• The side ,opposite, to the angle 69 degrees = y

,

• The side ,adjacent, to the angle 69 degrees = x

,

• The length of the ,hypotenuse, =23

Recall from trigonometric ratios that:

`\begin{gathered} \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \cos \theta=\frac{\text{Adjacent}}{\text{Hypotenuse}} \end{gathered}`

Therefore::

`\begin{gathered} \cos 69\degree=\frac{\text{x}}{\text{2}3} \\ x=23\cos 69 \\ x\approx8.2 \end{gathered}`

Similarly:

`\begin{gathered} \sin 69=\frac{\text{y}}{\text{2}3} \\ y=23\sin 69 \\ y\approx21.5 \end{gathered}`

The correct choice is B.