Given:
In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°.
To find:
The all possible values of ∠X, to the nearest degree.
Solution:
Law of Sines:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
For ΔWXY,
[tex]\dfrac{w}{\sin W}=\dfrac{x}{\sin X}=\dfrac{y}{\sin Y}[/tex]
Now,
[tex]\dfrac{w}{\sin W}=\dfrac{x}{\sin X}[/tex]
[tex]\dfrac{900}{\sin (157^\circ)}=\dfrac{680}{\sin X}[/tex]
[tex]900\sin X=680\sin (157^\circ)[/tex]
[tex]\sin X=\dfrac{680}{900}\sin (157^\circ)[/tex]
[tex]\sin X=0.295219[/tex]
[tex]X=\sin^{-1}(0.295219)[/tex]
[tex]X=17.17067[/tex]
[tex]X\approx 17[/tex]
Therefore, the value of ∠X is 17 degrees.
