Question

8 multiple choice 1 point find the value of the variable(s). if your answer is not an integer, leave it in simplest radical form. not drawn to scale ( x = 10, y = 20sqrt{3} ) ( x = 10sqrt{3}, y = 20 ) ( x = 20sqrt{3}, y = 10 ) ( x = 20, y = 10sqrt{3} )

Explanation:

Step1: Use the property of a 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, the side opposite the 30° angle is half the hypotenuse. Let the side opposite 30° be \(a\), the side opposite 60° be \(b\), and the hypotenuse be \(c\). The relationships are \(a=\frac{c}{2}\), \(b = a\sqrt{3}\).
Here, the side opposite 30° is \(10\) (the side with length \(10\) is opposite the 30° angle). So if \(y\) is the hypotenuse, then \(y = 2\times10=20\).

Step2: Find the value of \(x\)

The side \(x\) is opposite the 60° angle. Using the formula \(b=a\sqrt{3}\) (where \(a = 10\)), we get \(x=10\sqrt{3}\).

Answer:

\(x = 10\sqrt{3},y = 20\) (the second option)