Answer:
12 cm
Step-by-step explanation:
1. Consider right triangle MNK. In this triangle angle N is right and m∠M=60°, then m∠K=30°. Thus, this triangle is special 30°-60°-90° right triangle with legs MN and NK and hypotenuse MK=16 cm. The leg MN is opposite to the angle with measure of 30°, then this leg is half of the hypotenuse, MN=8 cm.
2. Consider right triangle MNH, where NH is the height of trapezoid drawn from the point N. In this triangle m∠M=60°, angle H is right, then m∠N=30°. Similarly, the leg MH is half of the hypotenuse MN, MH=4 cm.
3. Trapezoid MNOK is isosceles, because MN=OK=8 cm. This means that NO=MK-2MH=16-8=8 cm.
4. The midsegment of the trapezoid is
[tex]\dfrac{MK+NO}{2}=\dfrac{16+8}{2}=12\ cm.[/tex]
The mid segment of MNOK =12 cm
Let us consider right triangle MNK. In this triangle angle N is right and m∠M=60°, then m∠K=30°.
Thus, this triangle is special 30°-60°-90° right triangle
The shorter side is opposite the 30 degree angle, the longer side is opposite the 60 degree angle, and the hypotenuse is opposite the 90 degree angle.
with legs MN and NK and hypotenuse MK=16 cm. The leg MN is opposite to the angle with measure of 30°, then this leg is half of the hypotenuse, MN=8 cm.
Now, consider right triangle MNH, where NH is the height of trapezoid drawn from the point N.
In this triangle m∠M=60°, angle H is right, then m∠N=30°.
Similarly, the leg MH is half of the hypotenuse MN, MH=4 cm.
Trapezoid MNOK is isosceles,
because MN=OK=8 cm.
This means that,
NO=MK-2MH=16-8=8 cm.
The mid segment of the trapezoid is
[tex]\frac{MK+NO}{2}=\frac{16+8}{2} =12cm[/tex]
Therefore the mid segment is 12 cm.
To learn more about the mid segment visit:
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