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In ΔXYZ, ∠X=45° and ∠Y=83°. ∠XWZ=90° and XY=14. Find the length of XW to the nearest integer.

User Kirk Beard
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Answer: 14 units

Step-by-step explanation :To find the length of XW, we can use trigonometric ratios in right-angled triangle XWZ.

First, let’s find the measure of angle Z using the fact that the sum of angles in a triangle is 180°:

∠Z = 180° - ∠XWZ = 180° - 90° = 90°

Now, we can use the tangent ratio to find XW:

tan(∠X) = opposite/adjacent tan(45°) = XW/ZW 1 = XW/ZW

Since ZW is equal to XY (given that ZY is the hypotenuse of right-angled triangle XYZ), we can substitute XY = 14:

1 = XW/14 XW = 14

Therefore, the length of XW is 14 units.

User Noah Wilder
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