Question

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

Explanation:

Step1: Identify trigonometric relation

In right - triangle $PQO$ with right - angle at $P$, we know $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 24^{\circ}$, the adjacent side to $\theta$ is $x$ and the hypotenuse is $5.3$. So, $\cos(24^{\circ})=\frac{x}{5.3}$.

Step2: Solve for $x$

Multiply both sides of the equation $\cos(24^{\circ})=\frac{x}{5.3}$ by $5.3$. We get $x = 5.3\times\cos(24^{\circ})$.
Since $\cos(24^{\circ})\approx0.9135$, then $x = 5.3\times0.9135=4.84155$.

Step3: Round to the nearest tenth

Rounding $4.84155$ to the nearest tenth gives $x\approx4.8$.

Answer:

$4.8$