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

Explanation:

Step1: Identify the trigonometric relation

In right - triangle $WXY$ with right - angle at $Y$, we know $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 69^{\circ}$ and the side opposite to $\theta$ is $WY = 5.3$, and the side adjacent to $\theta$ is $XY$.

Step2: Set up the tangent formula

We have $\tan(69^{\circ})=\frac{WY}{XY}$. Since $\tan(69^{\circ})\approx2.605089$, and $WY = 5.3$, we can rewrite the formula as $2.605089=\frac{5.3}{XY}$.

Step3: Solve for $XY$

Cross - multiply to get $XY=\frac{5.3}{2.605089}\approx2.0$.

Answer:

$2.0$