Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $TYZ$, we know the adjacent side to the angle $68^{\circ}$ is $77$ and we want to find the hypotenuse $x$. We use the cosine function. $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(68^{\circ})=\frac{77}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\cos(68^{\circ}) = 77$. Then $x=\frac{77}{\cos(68^{\circ})}$.
Since $\cos(68^{\circ})\approx0.3746$, then $x=\frac{77}{0.3746}\approx205.55$.

Step3: Round the answer

Rounding $205.55$ to the nearest tenth gives $x\approx205.6$.

Answer:

$205.6$