Correct Answer is: Perimeter of ΔDMN is 54.873 units.
Solution:-
Given that DM=10√3,m∠M=75°,m∠N=45°
So,m∠D= 180-(75+45) = 60°
So to find perimeter we need other 2 sides also.
Let us use sine rule to find them.
[tex]\frac{DM}{sin(N)}=\frac{DN}{sin(M)} =\frac{MN}{sin(D)}[/tex]
[tex]\frac{10\sqrt{3} }{sin(45)} = \frac{DN}{sin(75)}=\frac{MN}{sin(60)}[/tex]
[tex]DN=\frac{10\sqrt{3} }{sin(45)}Xsin(75) = 23.66[/tex]
[tex]MN=\frac{10\sqrt{3} }{sin(45)} Xsin(60)=21.213[/tex]
Hence perimeter = DM+MN+DN
= 10+21.213+23.66
=54.873 units
