Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $UVW$ with $\angle U = 28^{\circ}$, the side adjacent to $\angle U$ is $UV = 4$ and the side opposite to $\angle U$ is $VW=x$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(28^{\circ})=\frac{x}{4}$.

Step2: Solve for $x$

Multiply both sides of the equation $\tan(28^{\circ})=\frac{x}{4}$ by 4. We get $x = 4\times\tan(28^{\circ})$.
Since $\tan(28^{\circ})\approx0.5317$, then $x = 4\times0.5317 = 2.1268$.

Step3: Round to the nearest tenth

Rounding $2.1268$ to the nearest tenth gives $x\approx2.1$.

Answer:

$2.1$