Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( XYZ \), \( \angle Z = 66^\circ \), \( YZ = 4 \) (adjacent side to \( \angle Z \)), and \( XY \) is the opposite side to \( \angle Z \). We use the tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \).

Step2: Set up the equation

Let \( XY = x \). Then \( \tan(66^\circ)=\frac{x}{4} \).

Step3: Solve for \( x \)

Multiply both sides by 4: \( x = 4\times\tan(66^\circ) \). Calculate \( \tan(66^\circ)\approx2.246 \), so \( x = 4\times2.246 = 8.984 \approx 9.0 \).

Answer:

\( 9.0 \)