Answer:
The answer to your question: Perimeter = 62.19 m
Step-by-step explanation:
Data
DM = 10 √3
∠M = 75°
∠N = 45
Perimeter = ?
Process
The 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
