In ΔXYZ, ∠X=83° and ∠Y=48°. ∠XWZ=90° and XY=4.6. Find the length of XW to the nearest 10th.
Answers
Answer:
\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines\put(0,0){\line(3,0){2cm}}\put(0,0){\line(0,3){2.7cm}}\put(10,0){\line(-3,4){2cm}}\put(-0.5,14){\textbf{\textsf{X}}}\put(-1,-2){\textbf{\textsf{Y}}}\put(10,-2){\textbf{\textsf{Z}}}\put(0,1){\line(3,0){2mm}}\put(1,0){\line(0,3){2mm}}\qbezier(0,10)(2,8)(2,10.4)\put(0.6,7.5){$\sf\footnotesize 60^\circ $}\put(7.5,5){\sf\footnotesize 20cm}\end{picture}
Solution :-
Using , trigonometric ratio "cos(X)"
Finding cos(X)
As we know that
cosA = Adjacent/hypotenuse .
Similarly
Substituting
Adjacent = Height = XY
Hypotenuse = 20cm
\to→ cos60° = XY/20
\to→ 1/2 = XY/20
• By cross multiplying
\to→ 20 = 2XY
\to→ XY = 20/2
\to→ XY = 10cm
Hence , XY = 10cm
Answer: 0.6
Step-by-step explanation: Delta Math said it was 0.6.