Question

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

Answer 1

The answer to your question: Perimeter = 62.19 m

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°

`(sin D)/(D)  = (sin M)/(N) =   (sin N)/(N)`

`(sin 60)/(D) = (sin45)/(10√(3) )`

D =
`(10√(3)sin 60 )/(sin 45)`

D = 21.21

}[/tex]

`(sin 75)/(M) = (sin45)/(10√(3) )`

D =
`(10√(3)sin 75 )/(sin 45)`

D = 23.66

Perimeter = 21.21 + 23.66 + 10
`√(3)`

Perimeter = 62.19 m