Question

solve for x. round to the nearest tenth, if necessary.
answer
attempt 1 out of 2
x =

Explanation:

Step1: Identify trigonometric ratio

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

Step2: Solve for $x$

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

Step3: Round the result

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

Answer:

$x = 3.1$