Question

the triangle below is equilateral. find the length of side ( x ) to the nearest tenth.

Explanation:

Step1: Define triangle properties

The large triangle is equilateral, so all sides = 12, all angles = $60^\circ$. The right triangle has hypotenuse 12, angle $60^\circ$, adjacent side $x$.

Step2: Use cosine function

Cosine of angle = adjacent/hypotenuse.
$\cos(60^\circ) = \frac{x}{12}$

Step3: Solve for x

Rearrange to isolate $x$.
$x = 12 \times \cos(60^\circ)$
$\cos(60^\circ) = 0.5$, so $x = 12 \times 0.5 = 6.0$

Answer:

6.0