In a right-angled triangle ABC, the height CH is drawn from the vertex of the right angle.

| July 10, 2021 | education

In a right-angled triangle ABC, the height CH is drawn from the vertex of the right angle. AB = 48 cm, AH = 12 cm.Find AC.

Let us determine the length of the segment AH.

AH = AB – AH = 48 – 12 = 36 cm.

Consider right-angled triangles ACH and CBH.

Let the value of the angle CAH = X0, then the angle ACH = (90 – X) 0.

Angle ACB = 90 by condition, then angle BCH = (90 – (90 – X)) = X0.

Then in the right-angled triangles ACH and BCH the acute angles CAH and BCH are equal, and then these triangles are similar in acute angle.

The ratio of the similar sides of similar triangles is equal. Then: AH / CH = CH / BH.

CH ^ 2 = AH * BH = 12 * 36 = 432.

From the right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the leg AC.

AC ^ 2 = CH ^ 2 + AH ^ 2 = 432 + 144 = 576.

AC = 24 m.

Answer: The length of the AC segment is 24 cm.



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