Question

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

Explanation:

Step1: Identify trigonometric ratio

We use the tangent ratio in right - triangle $YZT$. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 58^{\circ}$, the opposite side to $\theta$ is $YT = 6.7$ and the adjacent side is $YZ=x$. So, $\tan(58^{\circ})=\frac{YT}{YZ}=\frac{6.7}{x}$.

Step2: Solve for $x$

We know that $\tan(58^{\circ})\approx1.60033$. Then, from $\tan(58^{\circ})=\frac{6.7}{x}$, we can rewrite it as $x=\frac{6.7}{\tan(58^{\circ})}$.

Step3: Calculate the value of $x$

Substitute $\tan(58^{\circ})\approx1.60033$ into the formula: $x=\frac{6.7}{1.60033}\approx4.2$.

Answer:

$4.2$