Question

practice using trigonometric ratios to solve for missing lengths. which equation could be used to solve for the length xy? xy = (22)sin(41°) xy = (22)cos(41°) xy = \frac{22}{cos(41°)} xy = \frac{22}{sin(41°)}

Explanation:

Step1: Recall cosine ratio in right - triangle

In right - triangle $\triangle XYZ$ with right - angle at $Z$, $\cos Y=\frac{adjacent}{hypotenuse}$. Here, the adjacent side to angle $Y$ is $YZ = 22$ and the hypotenuse is $XY$.

Step2: Apply cosine formula

We know that $\cos(41^{\circ})=\frac{22}{XY}$.

Step3: Solve for $XY$

Cross - multiply to get $XY\times\cos(41^{\circ}) = 22$, then $XY=\frac{22}{\cos(41^{\circ})}$.

Answer:

$XY=\frac{22}{\cos(41^{\circ})}$