F.2 Maths(20點)

依上述文字所講,figure AB=7.5cm 是斜邊 ,∠ C ＝ 90ﾟ
∠ C ＝ 90ﾟ (Given)
BC^2 + AC^2 = AB^2 (Pythagoras' Theorem)
(4/3AC)^2 + AC^2 = 7.5^2
(25/9)AC^2 = 56.25
AC^2 = 20.25
AC = 4.5cm

Pythagoras' Theorem (畢氏定理) :

在直角三角形，
斜邊長度之平方 = 底邊長度之平方 + 高度之平方

斜邊 AB = 7.5cm [ sq(A) = A * A]

=> sq(AB) = sq(BC) + sq(AC)
=> 7.5 * 7.5 = sq(4/3AC) + sq(AC)
=> 56.25 = sq(4/3)sq(AC) + sq(AC)
=> 56.25 = 16/9sq(AC) + sq(AC)
=> 56.25 = sq(AC)*(16/9 + 1)
=> 56.25 = sq(AC)* (25/9)
=> sq(AC) = 56.25 * 9/25
=> sq(AC) = 20.25
=> AC = sqrt(20.25) [sqrt : square root]
=> AC = 4.25 cm

首先，你張圖在角ＢＣＡ應該是９０度，所以條識會是

ａｃ　ｓｑｕａｒｅ＋（４／３ａｃ）ｓｑｕａｒｅ　＝　ａｂ　ｓｑｕａｒｅ

唔ｗｒｉｔｅ太長　（　ｌｅｔ　ａｃ　ｓｑｕｑｒｅ　＝　Ｙ２）

Y2 + 1.7778Y2 = 56.25 (<呢個係7.5 SQUARE)

Y2 ( 1+1.7778) =56.25

Y2 = 56.25 / (1 + 1.7778)

Y2 = 20.2498

Y = 4.49998 ( < 把20.2498 開方）

所以　ａｃ　＝ 4.5CM

希望可以幫到你。