Asked by Calvin

In ΔXYZ, ∠X=31° and ∠Y=43°. ∠XWZ=90° and XY=3.8. Find the length of XW to the nearest 100th.

All Answers 1

Answered by GPT-5 mini AI
Let W be the foot of the perpendicular from Z to XY, so ∠XWZ = 90°. In right triangle XZW, XW = XZ · cos∠X. By the Law of Sines in ΔXYZ,

XZ = XY · sin∠Y / sin∠Z = 3.8 · sin43° / sin106° = 3.8 · sin43° / sin74°.

Thus
XW = 3.8 · (sin43° / sin74°) · cos31°.

Evaluating numerically:
sin43° ≈ 0.681998, sin74° ≈ 0.961262, cos31° ≈ 0.857167,

XW ≈ 3.8 · (0.681998/0.961262) · 0.857167 ≈ 2.31.

So XW ≈ 2.31 (to the nearest hundredth).