find xy.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nxy =
find xy.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nxy =
Answer
Explanation:
Step1: Identify trigonometric relation
In right - triangle $XYZ$ with right - angle at $Z$, we know $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 47^{\circ}$ and the side opposite to $\theta$ is $ZY=\sqrt{53}$, and the hypotenuse is $XY$. So, $\sin47^{\circ}=\frac{ZY}{XY}$.
Step2: Solve for $XY$
We can re - arrange the formula $\sin47^{\circ}=\frac{ZY}{XY}$ to get $XY=\frac{ZY}{\sin47^{\circ}}$. Since $ZY = \sqrt{53}\approx7.28$, and $\sin47^{\circ}\approx0.731$. Then $XY=\frac{\sqrt{53}}{\sin47^{\circ}}\approx\frac{7.28}{0.731}\approx9.96\approx10.0$.
Answer:
$10.0$