Answer:
[tex]MN=3.05\ units[/tex]
Step-by-step explanation:
we know that
The triangle ΔMNK, is an isosceles triangle, because has two equal sides, then has two equal angles
∠M =∠K
MN = MK
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
∠M + ∠N + ∠K = 180°
∠M=∠K
2∠M = 180° - 110°
∠M = 70°/2 = 35°
∠K=
∠M = 35°
see the attached figure to better understand the problem
Applying the law of sines determine the length side MN
[tex]\frac{sin(110\°)}{MK}=\frac{sin(35\°)}{MN}[/tex]
Solve for MN
[tex]MN=sin(35\°)(MK)/sin(110\°)[/tex]
substitute the values
[tex]MN=sin(35\°)(5)/sin(110\°)[/tex]
[tex]MN=3.05\ units[/tex]
