In triangle ABC, C = 90 degrees, B = 30 degrees, AC = 6 cm. Find the length of the median BM.
| September 7, 2021 | education
In a right-angled triangle ABC, the AC leg lies opposite angle 30, therefore, its length is equal to half the length of the hypotenuse AB. Then AB = 2 * AC = 2 * 8 = 12 cm.
By the Pythagorean theorem, we determine the length of the BC leg.
BC ^ 2 = AB ^ 2 – AC ^ 2 = 12 ^ 2 – 6 ^ 2 = 144 – 36 = 108.
BC = √108 = 6 * √3 cm.
Since, by condition, BM is the median, then AM = CM = AC / 2 = 6/2 = 3 cm.
From the right-angled triangle MBC, according to the Pythagorean theorem, we determine the length of the hypotenuse BM.
BM ^ 2 = BC ^ 2 + CM ^ 2 = (6 * √3) ^ 2 + 3 ^ 2 = 108 + 9 = 117.
BM = √117 = 3 * √13 cm.
Answer: The length of the median BM is 3 * √13 cm.
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