Question

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

Answer 1

if you're an RSM student, the answer is 3.052

Explanation:

draw an altitude from N to MK, splitting it from 5 into two parts that are 2.5 and 2.5

from there, you can label MN as x, but since MN = NK, NK can also be labeled as x

now, you can use sin

sin55 = 2.5/x; so x(sin55) = 2.5; so x = 2.5(sin55)

sin55 approximates to around 0.82; and then divide 2.5 by 0.82, and it'll round to approx 3.052

Answer 2

The length of MN is approximately 12.16.

Given that MN = NK and m∠N = 110º, we can conclude that △MNK is an isosceles triangle with ∠M = ∠K = (180º - 110º) / 2 = 70º.

Since MN = NK, we can draw a perpendicular line from point N to side MK, dividing MK into two equal segments, each with length 5/2.

Therefore, we have a right triangle with one leg (5/2) and the opposite angle (70º).

We can use the sine function to find the other leg (MN).

sin(70º) = MN / (5/2)

MN = (5/2) * sin(70º)

MN ≈ 12.16

Therefore, the length of MN is approximately 12.16.