Question

y =
short = hyple
short = long/√3
long = short * √3
hyp = short * 2

1. x=

y=

Explanation:

Step1: Identify the sides in a 30 - 60 - 90 triangle

In a right - angled triangle with angles \(30^{\circ}-60^{\circ}-90^{\circ}\), if the side opposite to \(30^{\circ}\) is \(a\) (short side), the side opposite to \(60^{\circ}\) is \(a\sqrt{3}\) (long side), and the hypotenuse is \(2a\). Here, the side opposite to \(60^{\circ}\) is \(11\sqrt{3}\). Let the side opposite to \(30^{\circ}\) be \(x\).
We know that \(\text{long}=\text{short}\times\sqrt{3}\). So, if \(\text{long}=11\sqrt{3}\), then \(11\sqrt{3}=x\times\sqrt{3}\).

Step2: Solve for \(x\)

Divide both sides of the equation \(11\sqrt{3}=x\times\sqrt{3}\) by \(\sqrt{3}\). We get \(x = 11\).

Step3: Solve for \(y\) (hypotenuse)

Since \(y = 2x\) (in a \(30 - 60 - 90\) triangle, hypotenuse \(=2\times\) short side). Substitute \(x = 11\) into the formula. So \(y=2\times11=22\).

Answer:

\(x = 11\), \(y = 22\)