Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trig - ratio

In right - triangle $OPQ$ with right - angle at $P$, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 53^{\circ}$, the opposite side to $\theta$ is $x$ and the adjacent side is $1.8$. So, $\tan(53^{\circ})=\frac{x}{1.8}$.

Step2: Solve for $x$

We know that $\tan(53^{\circ})\approx1.3270$. Then $x = 1.8\times\tan(53^{\circ})$. Substituting the value of $\tan(53^{\circ})$, we get $x=1.8\times1.3270 = 2.3886$.

Step3: Round to the nearest tenth

Rounding $2.3886$ to the nearest tenth gives $x\approx2.4$.

Answer:

$2.4$