Question

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

Answer 1

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,  

$\frac{m}{sinM} = \frac{n}{sinN} = \frac{k}{SinK}$

$\frac{k}{sinK} = \frac{n}{sinN}$

$\frac{5}{sin 110^{\circ}} = \frac{k}{sin 35^{\circ}}$

$k = \frac{5 sin 35^{\circ}}{sin 110^{\circ}}$

Now ∵ sin 35° = 0.57 and sin 110° = 0.94 approx.

By substituting these values in above expression,

$k = \frac{5 \times 0.57}{0.94}$

k = $\frac{2.85}{0.94}$

k = 3.03

Therefore, MN = 3 approx.