In the MOT triangle, the angle is O = 90 *, the angle is T = 30 *. From the angle O, the median OC

In the MOT triangle, the angle is O = 90 *, the angle is T = 30 *. From the angle O, the median OC is drawn to the side of the MT. MO = 13 cm. Find the length of the median OK.

In a right-angled triangle, the leg opposite an angle of 30 ° is equal to half the hypotenuse. Hence ОМ = ½ ТМ.

TM = 2 OM = 2 * 13 = 26 (cm).

Because OK is the median, then TC = KM.

So KM = ½ TM = ½ * 26 = 13 (cm).

Consider the OCM triangle. In it KM = OM. Therefore, the triangle is isosceles.

∠М = 90 ° – 30 ° = 60 °.

∠MKO = ∠KOM = (180 ° – 60 °): 2 = 60 °.

So the OKM triangle is equilateral.

OK = KM = OM = 13 cm.

Answer: the median length is OK 13 cm.