Answer:
MN = 3.03 ≈ 3
Step-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.
