solve for $x$. round to the nearest tenth, if necessary.\nanswer\nattempt 1 out of 3\n$x = $

Explanation:

Step1: Identify trig - ratio

In right - triangle $\triangle HIJ$, we know the adjacent side to the given angle $\angle H = 27^{\circ}$ is $HI = 6$ and we want to find the opposite side $IJ=x$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(27^{\circ})=\frac{x}{6}$.

Step2: Solve for $x$

Multiply both sides of the equation $\tan(27^{\circ})=\frac{x}{6}$ by 6. We get $x = 6\times\tan(27^{\circ})$. We know that $\tan(27^{\circ})\approx0.5095$. Then $x=6\times0.5095 = 3.057$.

Step3: Round the answer

Rounding $3.057$ to the nearest tenth gives $x\approx3.1$.

Answer:

$3.1$