Given a right-angled triangle MNK angle K 90 degrees KM 6 centimeters NK root 6 of 3 KD median. find the angle KDM.

univerkov | February 5, 2021 | education

In a right-angled КDM triangle, according to the Pythagorean theorem, we determine the length of the hypotenuse MН.

MH ^ 2 = MK ^ 2 + KH ^ 2 = 36 + 108 = 144.

MH = 12 cm.

Since CD is the median of a right-angled triangle by МНК, drawn to the hypotenuse, its length is equal to half the length of the hypotenuse of the MН.

KD = MD = ND = MD / 2 = 12/2 = 6 cm.

In the MKD triangle, MK = MD = KD = 6 cm, then the MKD triangle is equilateral, and all its angles are 60.

Then the angle KDM = 60.

Answer: The КDM angle is 60.

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