In a right-angled triangle MNK, angle K = 90, KM = 6 cm, NK = 6√3, KD-median. Find the angle KDM.

univerkov | August 15, 2021 | education

By the Pythagorean theorem, we determine the length of the HM hypotenuse.

HM ^ 2 = KM ^ 2 + HK ^ 2 = 36 + 108 = 144.

NM = 12 cm.

According to the property of the median of a right-angled triangle, drawn from the vertex of the right angle, its length is equal to half the length of the hypotenuse.

Then KD = NM / 2 = 12/2 = 6 cm.

In the KDM triangle: KM = 6 cm, KD = 6 cm, DM = NM / 2 = 6 cm, therefore, the KDM triangle is equilateral, and then all its internal angles are 60.

Answer: KDM angle = 600.

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