aleidam2022
Answered

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In ΔXYZ, ∠X=82° and ∠Y=84°. ∠XWZ=90° and XY=97. Find the length of XW to the nearest integer.

In ΔXYZ X82 And Y84 XWZ90 And XY97 Find The Length Of XW To The Nearest Integer class=

Sagot :

Check the picture below to the left, let's use those sides with the law of sines

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(14^o)}{97}=\cfrac{sin(84^o)}{XZ}\implies XZ = \cfrac{97\cdot sin(84^o)}{sin(14^o)}\implies XZ \approx 398.76 \\\\\\ \stackrel{\textit{now using SOH CAH TOA}}{cos(82^o) = \cfrac{XW}{XZ}}\implies XZcos(82^o)=XW \\\\\\ 398.76cos(82^o)\approx XW\implies 55.497\approx XW\implies \stackrel{\textit{rounded up}}{55=XW}[/tex]

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