The height CD, drawn from the top of the right angle C of the right-angled triangle ABC
March 27, 2021 | education
| The height CD, drawn from the top of the right angle C of the right-angled triangle ABC, is 12 cm, and the segment AD = 9 cm. What is the segment BD?
Let us prove that triangles ACD and BCD are similar.
Let the angle CAB = α, then the angle ACD = 90 – α.
Angle ВСD = АВС – АСD = 90 – (90 – α) = α.
Angle CAD = BCD, right-angled triangles ACD and BCD are similar in acute angle.
Then AD / CD = CD / BD.
CD ^ 2 = AD * BD.
ВD = СD ^ 2 / АD = 12 ^ 2/9 = 144/9 = 16 cm.
Answer: The length of the segment BD = 16 cm.
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