In a right-angled triangle MNK, angle K = 90 °, MK = 6cm, angle MNK = 30 °. Find MN and KN.

Based on the condition of this problem, the MN side will be the hypotenuse.

As we know from the school geometry course, the leg that is opposite the 30 ° angle will be half the length of the hypotenuse.

The MK side is opposite such an angle, therefore, the MN side will be equal to:

6 * 2 = 12.

Let us find out how many centimeters the length of the other leg of the indicated triangle is expressed, for which we use the well-known equation from the Pythagorean theorem:

√ (12 ^ 2 – 6 ^ 2) = √ (6 * 18) = 6√3.

Answer: MN = 12 cm, KN = 6√3 cm.

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