Given: mnok is a trapezoid, mn=ok, m∠m=60°, nk ⊥ mn , mk=16cm find: the midsegment of mnok. need now will give 15 points

 24 unit

Step-by-step explanation:

Here,  MNOK is a trapezoid, MN=OK, m∠M=60°, NK ⊥ MN , MK=16cm

Since, a mid segment is the line segment which joins the mid points of the equal sides of the isosceles trapezoid.

Let LO is the mid segment of trapezoid  MNOK

Where, Let J is the intersection point of KN and LO.

Therefore, LO= LJ+JO --------(1)

And, KL=LO , MO=ON

Since, In triangle KLJ,

∠LKJ=90° ( given),  ∠KLJ=60° ( because, LO║ON and it is given m∠M=60°)

Thus, ∠KJL=30°

Therefore, sin 30°=LK/LJ=8/LJ ( Because ΔMKN is a isoceleus triangle where ∠MKN=∠MNK=30°⇒KM=MN)

⇒LJ=8×2=16

Now, In ΔNOJ,

∠ONJ=∠OJN=30°

Therefore, ON=OJ ( by the property of isosceles triangle)

⇒OJ=8

Thus, By putting these values in equation 1) we get,

LO=16+8=24 cm

astronomers is your final answer! : )