Question

the triangle below is equilateral. find the length of side x in simplest radical form with a rational denominator. 8 x answer attempt 1 out of 2 x = submit answer √

Explanation:

Step1: Identify triangle properties

The triangle is equilateral, so all angles are 60°. The right triangle formed has angle 60°, hypotenuse equal to side length, and opposite side 8.

Step2: Apply sine formula

$\sin(60^\circ) = \frac{8}{s}$, where $s$ is side length. $\sin(60^\circ)=\frac{\sqrt{3}}{2}$, so $\frac{\sqrt{3}}{2}=\frac{8}{s}$ → $s=\frac{16}{\sqrt{3}}$.

Step3: Rationalize denominator

$s=\frac{16\sqrt{3}}{3}$. The right triangle's adjacent side $x = s\cos(60^\circ)=\frac{16\sqrt{3}}{3}×\frac{1}{2}=\frac{8\sqrt{3}}{3}$.

Answer:

$\frac{8\sqrt{3}}{3}$