Question

what are x and y in this 30 - 60 - 90 triangle? x = 6 y = 3√2 x = 6 y = 3√3 x = 3√3 y = 6 x = 3√2 y = 3

Explanation:

Step1: Recall 30 - 60 - 90 triangle side ratios

In a 30 - 60 - 90 triangle, if the side opposite the 30° angle is \(a\), the side opposite the 60° angle is \(a\sqrt{3}\), and the hypotenuse is \(2a\). Here, the side adjacent to the 60° angle (which is opposite the 30° angle) is \(3\). So \(a = 3\).

Step2: Find the hypotenuse \(x\)

Using the ratio for the hypotenuse (\(2a\)), we have \(x=2\times3 = 6\).

Step3: Find the side \(y\) (opposite 60°)

Using the ratio \(a\sqrt{3}\), with \(a = 3\), we get \(y = 3\sqrt{3}\).

Answer:

\(x = 6\) and \(y=3\sqrt{3}\) (corresponding to the second option \(x = 6,y = 3\sqrt{3}\))