find uw. write your answer as an integer or as a decimal rounded to the nearest tenth. uw =

Explanation:

Step1: Identify trigonometric relation

In right - triangle $UW V$, we know $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 51^{\circ}$, the adjacent side to $\angle V$ is $WV = 2.4$, and the opposite side is $UW$. So, $\tan(51^{\circ})=\frac{UW}{WV}$.

Step2: Solve for $UW$

Since $WV = 2.4$ and $\tan(51^{\circ})\approx1.2349$, then $UW=WV\times\tan(51^{\circ})$. Substituting the value of $WV$, we get $UW = 2.4\times1.2349$. $UW=2.4\times1.2349 = 2.96376$.

Step3: Round the result

Rounding $2.96376$ to the nearest tenth, we get $3.0$.

Answer:

$3.0$