In the right-angled triangle ABC (c = 90 °) the height CH is drawn. Find BH if AH = 16, cosA = 3/4.

Since CH is the height, the ACH triangle is rectangular.

In a right-angled triangle ACH CosCAH = AH / AC.

3/4 = AH / AC.

AC = 4 * AH / 3 = 4 * 16/3 = 64/3 cm.

In a right-angled triangle ACH, according to the Pythagorean theorem, CH ^ 2 = AC ^ 2 – AH ^ 2 = 4096/9 – 256 =

(4096 – 2304) / 9 = 1792/9.

CH – the height drawn from the top of the right angle to the hypotenuse, then:

CH ^ 2 = AH * BH.

BH = CH ^ 2 / AH = (1796/9) / 16 = 112/9 = 12 (4/9) cm.

Answer: The length of the segment BH is 12 (4/9) cm.