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我有兩題數學要大家幫手

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http://hk.pg.photos.yahoo.com/ph/quetions2007/detail?.dir=9492scd&.dnm=a817scd.jpg&.src=ph 請大家入以上這個網址,有題目嫁lA 請詳列步驟. 更新: 有兩題嫁 第一題,分a,b , 然後按一頁有下一題

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a) Consider △ACH, tan 60° = h / AC AC = h / tan 60° AC = h / sqrt 3 // Consider △BCH, tan 30° = h / BC BC = h / tan 30° BC = h / (1 / sqrt 3) BC = (sqrt 3)h // As AB=AC+BC,thus AB = h / sqrt 3 + (sqrt 3)h = 4h / sqrt 3 // b) using the result of (a), AB = 4h / sqrt 3 2000 = 4h / sqrt 3 h = 2000(sqrt 3)/4 = 500(sqrt 3) = 866m // (cor. to the nearest m) 2007-04-08 12:13:24 補充： 樓上那位,你說AC = (tan60)h , BC = (tan30)h那 AC 豈不是會大過BC?但按常理,angle of elevation(仰望角)越大,代表那物件越高, 或水平距離越近所以, AC 2007-04-08 12:14:50 補充： 所以, AC 2007-04-08 12:18:36 補充： 所以, AC 小於 BC 才是對的. (符號顯示不出)另外,tan x = "opposite side of x" / "adjacent side of x"至於你最終答案和我一樣,是因為tan 60° tan 30° = 1/tan 30° 1/tan 60° = 1/tan 60° 1/tan 30°所以,你倒置了兩個tan 對答案沒有影響.但問題出於AC和BC的數值身上.而我的答案, AC = h / sqrt 3 和 BC = (sqrt 3)h 才是對的.

其他解答:

a> consider triangle ACH AC / h = tan60 AC = (tan60)h consider triangle BCH BC / h = tan 30 BC = (tan30)h AC + BC = AB so AB = (tan 60)h + (tan30)h = h(tan 60 + tan30) b> sqrt means square root h(tan 60 + tan30) = 2000 we know that tan 60 = sqrt(3) and tan 30 = 1 / sqrt(3) h = 2000 / (sqrt(3) + 1 / sqrt(3)) = sqrt(3) 2000 / (3 + 1) (multiply both quotient and divisor by sqrt(3)) = 500 sqrt(3) 2007-04-08 12:44:20 補充： 係喎, 調轉o左唔好意思