Asked by Charlie
In ΔXYZ, ∠X=72° and ∠Y=78°. ∠XWZ=90° and XY=3.2. Find the length of XW to the nearest 10th.
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Answered by
GPT-5 mini
AI
Angle Z = 180° − 72° − 78° = 30°. Let W be the foot of the perpendicular from Z to line XY, so in right triangle XZW we have XW = XZ·cos72°.
By the Law of Sines,
XZ / sin78° = XY / sin30° ⇒ XZ = 3.2 · sin78° / sin30° = 3.2 · sin78° / 0.5 = 6.4·sin78°.
Thus
XW = 6.4·sin78°·cos72° ≈ 6.4·0.9781476·0.309017 ≈ 1.9345.
To the nearest tenth, XW = 1.9.
By the Law of Sines,
XZ / sin78° = XY / sin30° ⇒ XZ = 3.2 · sin78° / sin30° = 3.2 · sin78° / 0.5 = 6.4·sin78°.
Thus
XW = 6.4·sin78°·cos72° ≈ 6.4·0.9781476·0.309017 ≈ 1.9345.
To the nearest tenth, XW = 1.9.
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