Given: △DMN, DM=10 square root 3, m∠M=75°, m∠N=45° Find: Perimeter of △DMN

Answer:The answer to your question:  Perimeter = 62.19 mStep-by-step explanation:DataDM = 10 √3∠M = 75°∠N = 45Perimeter = ?ProcessThe sum of the internal angles in a triangles equals 180°                         ∠D + ∠M + ∠N = 180                           ∠D = 75 + 45 = 180                            ∠D = 180 - 120                             ∠D = 60°[tex]\frac{sin D}{D}  = \frac{sin M}{N} =   \frac{sin N}{N}[/tex][tex]\frac{sin 60}{D} = \frac{sin45}{10\sqrt{3} }[/tex]D = [tex]\frac{10\sqrt{3}sin 60 }{sin 45}[/tex]D = 21.21       [tex]\frac{sin D}{D}  = \frac{sin 75}{M} =   \frac{sin 45}{10[tex]\sqrt{3}[/tex]}[/tex][tex]\frac{sin 75}{M} = \frac{sin45}{10\sqrt{3} }[/tex]D = [tex]\frac{10\sqrt{3}sin 75 }{sin 45}[/tex]D = 23.66 Perimeter = 21.21 + 23.66 + 10[tex]\sqrt{3}[/tex]Perimeter = 62.19 m