△ABC is a right-angled triangle, where ∠ACB = 90° . CD is the altitude of AB in △ABC.
A1. Prove that △BCD ～ △CAD
A2. Hence, show that CD^2 = AD*DB
B. If AD = 4cm & DB = 9cm, find AC & BC.
(leave your answers in surd form)
F.3 maths
2008-12-28 11:35 pm
回答 (1)
2008-12-28 11:55 pm
✔ 最佳答案
A1It is obviously that △ABC ～ △CBD (AAA) and △ABC ～ △ACD (AAA)
So △CBD ～ △ACD or △BCD ～ △CAD
A2
AD/CD=BD/CD
So CD^2 = AD*DB
B
AD = 4cm & DB = 9cm
CD=6 cm
AC^2=AD^2+CD^2=16+36=52
So AC=SQRT(52)
BC^2=BD^2+CD^2=81+36=117
So BC=SQRT(117)
收錄日期: 2021-04-25 16:58:37
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https://hk.answers.yahoo.com/question/index?qid=20081228000051KK01048