In a femoral triangle with an angle at the base of 30 and the base of 12 cm, find 1) the lateral side

| August 2, 2021 | education

In a femoral triangle with an angle at the base of 30 and the base of 12 cm, find 1) the lateral side 2) the median drawn to the base 3) the median drawn to the lateral side

The median BH, drawn to the base, is also the height of the triangle, then the triangle ABH is rectangular in which the leg AH = AC / 2 = 12/2 = 6 cm.

tgA = BH / AH.

BH = AH * tg30 = 6 * 1 / √3 = 2 * √3 cm.

AB ^ 2 = AH ^ 2 + BH ^ 2 = 36 + 12 = 48.

AB = 4 * √3 cm.

The medians, at the point of their intersection, are divided in a ratio of 2/2, starting from the top, then BO = 2 * OH. BO + OH = BH.

BH = 2 * OH + OH = 3 * OH = 2 * √3.

OH = 2 * √3 / 3.

In a right-angled triangle AOН, AO ^ 2 = AH ^ 2 + OH ^ 2 = 36 + 12/9 = 36 + 4/3 = 112/3.

AO = 4 * √7 / √3 = 4 * √21 / 3.

Then OK = AO / 2 = 2 * √21 / 3.

AK = AР + OK = 2 * √21 cm.

Answer: The median BH is 2 * √3 cm, the side side is 4 * √3 cm, the median AK is 2 * √21 cm.



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