Answer:
≈ 35.91
Step-by-step explanation:
The law of sines lets you find the other sides:
DN/sin(M) = MN/sin(D) = DM/sin(N)
Angle D is 180° -75° -45° = 60°, so the remaining sides are ...
DN = sin(M)/sin(N)×DM = sin(75°)/sin(45°)×10 ≈ 13.66
MN = sin(D)/sin(N)×DM = sin(60°)/sin(45°)×10 ≈ 12.25
The perimeter is the sum of the side lengths, so is ...
10 + 13.66 +12.25 = 35.91
Answer:
35.91 units ( approx )
Step-by-step explanation:
Given,
In triangle DMN,
DM = 10
, m∠M = 75°, m∠N = 45°,
By the law of sine,
[tex]\frac{\sin M}{DN}=\frac{\sin N}{MD}=\frac{\sin D}{MN}----(1)[/tex]
∵ m∠M + m∠N + m∠D = 180°,
75° + 45° + m∠D = 180°,
120° + m∠D = 180°
⇒ m∠D = 60°,
From equation (1),
[tex]\frac{\sin 75}{DN}=\frac{\sin 45}{10}=\frac{\sin 60}{MN}[/tex]
[tex]\frac{\sin 75}{DN}=\frac{\sin 45}{10}[/tex]
[tex]\implies DN = \frac{10\times \sin 75}{\sin 45}\approx 13.66\text{ unit}[/tex],
[tex]\frac{\sin 45}{10}=\frac{\sin 60}{MN}[/tex]
[tex]\implies MN = \frac{10\times \sin 60}{sin 45}\approx 12.25\text{ unit}[/tex]
Hence, the perimeter of the triangle DMN = DM + MN + DN
= 10 + 13.66 + 12.25
= 35.91 units.
