Question

find xy.
triangle with right angle at x, angle at w is 58 degrees, side wx is √23
write your answer as an integer or as a decimal rounded to the nearest tenth.
xy =
submit

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( WXY \), we know angle \( W = 58^\circ \), side \( WX=\sqrt{23} \), and we need to find \( XY \). We can use the tangent function, since \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). Here, \( \theta = 58^\circ \), opposite side to \( \theta \) is \( XY \), and adjacent side is \( WX \). So \( \tan(58^\circ)=\frac{XY}{WX} \).

Step2: Solve for \( XY \)

We know \( WX = \sqrt{23}\approx4.796 \). Then \( XY = WX\times\tan(58^\circ) \). Calculate \( \tan(58^\circ)\approx1.6003 \). So \( XY\approx4.796\times1.6003 \approx 7.7 \) (rounded to the nearest tenth).

Answer:

\( 7.7 \)