Question

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

Explanation:

Step1: Use tangent function

In right - triangle $NOP$, $\tan P=\frac{NO}{OP}$. Given $\angle P = 69^{\circ}$ and $OP = 80$, and $NO=x$. The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan69^{\circ}=\frac{x}{80}$.

Step2: Solve for $x$

We know that $\tan69^{\circ}\approx2.605089$. Then, $x = 80\times\tan69^{\circ}$. Substituting the value of $\tan69^{\circ}$, we get $x=80\times2.605089 = 208.40712$.

Step3: Round to the nearest tenth

Rounding $208.40712$ to the nearest tenth gives $x\approx208.4$.

Answer:

$208.4$