45.20Use the law of sines to find the value of y. Round to thenearest tenthLaw of sines: sin(A) = sin(B) = sin(C)1.4 units1.6 units2.5 units2.6 units
Accepted Solution
A:
Answer: 2.5 unitsStep-by-step explanation:Asuming we have a triangle [tex]XYZ[/tex], where:[tex]XY=2 units[/tex][tex]XZ=Y[/tex], hence [tex]Z=XY=2 units[/tex]Angle [tex]A[/tex] for [tex]Y[/tex] is [tex]A=75\°[/tex] Angle [tex]B[/tex] for [tex]Z[/tex] is [tex]B=50\°[/tex] We have to apply the law of sines:[tex]\frac{sin A}{Y}=\frac{sin B}{Z}=\frac{sin C}{X}[/tex]Then:[tex]\frac{sin 75\°}{Y}=\frac{sin 50\°}{2 units}[/tex]Isolating [tex]Y[/tex]:[tex]Y=\frac{(2units)sin 75\°}{sin 50\°}[/tex][tex]Y=2.5 units[/tex]