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

Answer 1

Since MN=NK, draw an isosceles triangle (two sides are equal). Mark the angle N as 110 degrees. Now, draw a line from N to the opposite side at a right angle. This line will divide MK=5 in half since MN = NK. It will also divide angle N into half. So, we will end up with a right triangle with one side 5/2 = 2.5 and the opposite angle 55 degrees.

sin(55) = opposite / hypotenuse = 2.5 / MN = 0.82

MN = 2.5 / 0.82 = 3.05