Question

find x rounded to one decimal place. x = 30° 2 x

Explanation:

Step1: Find the hypotenuse of the small - right triangle

In the small right - triangle with side length 2, if we consider the angle of 30°. We know that $\sin30^{\circ}=\frac{2}{h_1}$, where $h_1$ is the hypotenuse of the small right - triangle. Since $\sin30^{\circ}=\frac{1}{2}$, then $h_1 = 4$.

Step2: Find the length of the adjacent side of the large right - triangle

In the large right - triangle, the angle is 30° and the hypotenuse is $h_1 = 4$. We use the tangent function. $\tan30^{\circ}=\frac{x}{h_1}$. Since $\tan30^{\circ}=\frac{\sqrt{3}}{3}$ and $h_1 = 4$, then $x = 4\times\tan30^{\circ}=\frac{4\sqrt{3}}{3}\approx2.3$.

Answer:

$2.3$