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.
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