In a right-angled triangle MNK, N = 90 degrees, K = 60 degrees, MK = 10 cm. Find leg NK.

1. We calculate the value of the angle M, based on the fact that the total value of all internal angles of the triangle is 180 °.

Angle M = 180 ° – 60 ° – 90 ° = 30 °.

2. In accordance with the properties of a right-angled triangle, the length of the leg, located opposite the angle of 30 °, is equal to half the length of the hypotenuse. Using this property, we calculate the length of the leg NK, which is opposite the angle M, equal to 30 °:

NK = MK / 2 = 10: 2 = 5 centimeters.

Answer: the length of the leg NK is 5 centimeters.