In a right-angled triangle MNK, angle K = 90 °, MK = 6cm, angle MNK = 30 °. Find MN and KN.
| June 30, 2021 | education
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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