In an acute-angled triangle ABC, the projections of the lateral sides AB and BC to the base AC

| September 1, 2021 | education

In an acute-angled triangle ABC, the projections of the lateral sides AB and BC to the base AC are equal to 2 and 4. Find the projection of the median AD to the base AC.

The projection of the side AB onto the base of the AC is the segment AH = 2 cm.

The projection of the BC side onto the AC base is the segment СН = 4 cm.

The median AD divides the BC side in half, CM = ВM.

Let us lower the perpendicular from point M to the base of the AC.

The segment AK is the required distance.

Since BH is the height of the triangle ABC, and MK is perpendicular to the AC, then MK is parallel to BH, and then MK is the middle line of the triangle CBH, and then CK = HK = CH / 2 = 4/2 = 2 cm.

Then AK = AН + НK = 2 + 2 = 4 cm.

Answer: The projection of the median AM on the base of the AC is 4 cm.



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