Question

Find the value of x and the value of y.A. x = 15, y = 10sqrt3B. r = 20, y = 10sqrt3C. r = 20sqrt3, y = 5sqrt3D. x=15, y = 5sqrt3

Answer 1

To find the values of x and y it is necessary to use trigonometric ratios.

To find x it is necessary to use sine. Sine is the ratio between the opposite side to a given angle and the hypotenuse. In this case, the given angle is 60°, the opposite side is x and the hypotenuse is 10 sqrt 3. Use this information to find x:

`\begin{gathered} \sin 60=\frac{x}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\sin 60=x \\ x=15 \end{gathered}`

To find y it is necessary to use cosine. It is the ratio between the adjacent side to a given angle and the hypotenuse. The given angle is 60°, the adjacent side is y and the hypotenuse is 10 sqrt 3. Follow the same procedure as with sine:

`\begin{gathered} \cos 60=\frac{y}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\cos 60=y \\ y=5\sqrt[]{3} \end{gathered}`

The correct answer is D. x=15, y=5sqrt3.