Question

In △MNK MN = NK, m∠N = 110º, MK = 5. Find MN.

Answer 1

Answer:

$MN=3.05\ units$

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

$\frac{sin(110\°)}{MK}=\frac{sin(35\°)}{MN}$

Solve for MN

$MN=sin(35\°)(MK)/sin(110\°)$

substitute the values

$MN=sin(35\°)(5)/sin(110\°)$

$MN=3.05\ units$