Question

find the value of x.

x
x = ?

Explanation:

Step1: Identify side-angle relationship

In a 30-60-90 right triangle, the side opposite the 30° angle is half the hypotenuse, and the side opposite 60° is $\frac{\sqrt{3}}{2}$ times the hypotenuse. Here, $x$ is opposite the 30° angle? No, wait: the hypotenuse is 12, $x$ is adjacent to 60° and opposite 30°? Wait no: angle at top is 60°, so $x$ is adjacent to 60°, opposite 30°. The side opposite 30° is $\frac{1}{2}$ hypotenuse.
Wait, correction: hypotenuse $c=12$. The side opposite 30° is $\frac{c}{2}$, and side opposite 60° is $\frac{c\sqrt{3}}{2}$.
Looking at the triangle: the 30° angle is at the bottom right, so its opposite side is $x$.

Step2: Calculate x

$x = \frac{1}{2} \times \text{hypotenuse}$
$x = \frac{1}{2} \times 12$
Or, using cosine: $\cos(60^\circ) = \frac{x}{12}$, so $x = 12 \times \cos(60^\circ) = 12 \times \frac{1}{2}$

Answer:

$6$