Question

find the value of x.
8√3
30°
60°
x
x = ?

Explanation:

Step1: Identify triangle type

This is a 30 - 60 - 90 right - triangle. In a 30 - 60 - 90 triangle, the sides are in the ratio \(1:\sqrt{3}:2\), where the side opposite \(30^{\circ}\) is the shortest side (let's call it \(a\)), the side opposite \(60^{\circ}\) is \(a\sqrt{3}\), and the hypotenuse (opposite \(90^{\circ}\)) is \(2a\).

Step2: Determine the side opposite \(60^{\circ}\)

The side with length \(8\sqrt{3}\) is opposite the \(60^{\circ}\) angle. From the ratio, if the side opposite \(60^{\circ}\) is \(a\sqrt{3}\), and here \(a\sqrt{3}=8\sqrt{3}\), then we can solve for \(a\) by dividing both sides by \(\sqrt{3}\). So \(a = 8\).

Step3: Find the hypotenuse (x)

The hypotenuse (which is \(x\) in this case, as it is opposite the right - angle) is \(2a\). Since \(a = 8\), then \(x=2\times8 = 16\).

Answer:

16