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

Answer:MN = 3.03 ≈ 3Step-by-step explanation:Given: In ΔMNK MN = NK , m∠N = 110° and MK = 5.To find: MN = ?Sol: In ΔMNK,∠M + ∠N + ∠K = 180°  (sum of angles of a triangle)2∠M = 180° - 110°  ( ∠M =∠K since MN = MK)∠M = 70°/2 = 35°∴ ∠M = ∠K = 35°Now, Using Sine Rule for finding sides,  [tex]\frac{m}{sinM} = \frac{n}{sinN} = \frac{k}{SinK}[/tex][tex]\frac{k}{sinK} = \frac{n}{sinN}[/tex][tex]\frac{5}{sin 110^{\circ}} = \frac{k}{sin 35^{\circ}}[/tex][tex]k = \frac{5 sin 35^{\circ}}{sin 110^{\circ}}[/tex]Now ∵ sin 35° = 0.57 and sin 110° = 0.94 approx.By substituting these values in above expression,[tex]k = \frac{5 \times 0.57}{0.94}[/tex]k = [tex]\frac{2.85}{0.94}[/tex]k = 3.03 Therefore, MN = 3 approx.