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題目:In the figure, Sammi and Andy are 170m apart. There is a lamp-post between them. Sammi, Andy and the lamp-post form a straight line. Find the height of the lamp-post.Figure:~~~~~~~~~~~~~~top of the... 顯示更多 題目: In the figure, Sammi and Andy are 170m apart. There is a lamp-post between them. Sammi, Andy and the lamp-post form a straight line. Find the height of the lamp-post. Figure: ~~~~~~~~~~~~~~top of the lamp-post ~~~~~~~~~~／~~~~~~~~~~~~~~~~~＼~~~~~~ ~~~~~~~~／~~~~~~~~~~~~~~~~~~~~~＼~~~ ~~~~~~／~~~~~~~~~~~~~~~~~~~~~~~~~＼~~~~~ Andy∠35°~~~~~~~~Lamp-post~~~~~~~~40°＼Sammi 老師話要用sin cos tan 唔識計

最佳解答:

Let (X)m be the length between Andy and Lamp-post, (170-X)m be the length between Sammi and Lamp-post, (Y)m be the height of the lamp-post. Because Y/X = tan35 Y = tan35 x X and Y/(170-X) = tan40 Y = tan40 x (170-X) So tan35 x X = tan40 x (170-X) 0.700 x X = 0.839 x (170-X) 0.700X = 0.839 x 170 - 0.839 x X 0.700X = 142.63 - 0.839X 0.700X + 0.839X = 142.63 1.539X = 142.63 X = 92.677 Height of Lamp-post: Y/X = tan35 Y/92.677 = tan35 Y/92.677 = 0.700 Y = 0.700 x 92.677 Y = 64.87 So, the height of the lamp-post is 64.87m.

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其他解答:

Mathod 1 Let Point A is Andy Let Point L is Lamp post Let Point S is Sammi Let Point T is the top of the lamp post Then ATS is a triangle with angle A = 35° and angle S is 40° Also TL bisect the triangle into two right angle triangles at T Hence we have two equations tan 35 = TL / AL ...............1 tan 40 = TL / (170-AL)......2 from 1 AL = TL / tan 35 from 2 AL = 170 - TL / tan 40 therefore TL / tan 35 = 170 - TL / tan 40 TL tan 40 = 170 x tan35 x tan 40 - TL tan 35 TL (tan 40 + tan 35) = 170 x tan 35 x tan 40 TL = 170 x tan 35 x tan 40 / (tan 40 + tan 35) Mathod 2 Let (X)m be the length between Andy and Lamp-post, (170-X)m be the length between Sammi and Lamp-post, (Y)m be the height of the lamp-post. Because Y/X = tan35 Y = tan35 x X and Y/(170-X) = tan40 Y = tan40 x (170-X) Therefore tan35 x X = tan40 x (170-X) 0.700 x X = 0.839 x (170-X) 0.700X = 0.839 x 170 - 0.839 x X 0.700X = 142.63 - 0.839X 0.700X + 0.839X = 142.63 1.539X = 142.63 X = 92.677 Height of Lamp-post: Y/X = tan35 Y/92.677 = tan35 Y/92.677 = 0.700 Y = 0.700 x 92.677 Y = 64.87 Therefore, the height of the lamp-post is 64.87m.|||||題目係咪仲有些條件未寫?|||||Let Point A is Andy Let Point L is Lamp post Let Point S is Sammi Let Point T is the top of the lamp post Then ATS is a triangle with angle A = 35° and angle S is 40° Also TL bisect the triangle into two right angle triangles at T Hence we have two equations tan 35 = TL / AL ...............1 tan 40 = TL / (170-AL)......2 from 1 AL = TL / tan 35 from 2 AL = 170 - TL / tan 40 therefore TL / tan 35 = 170 - TL / tan 40 TL tan 40 = 170 x tan35 x tan 40 - TL tan 35 TL (tan 40 + tan 35) = 170 x tan 35 x tan 40 TL = 170 x tan 35 x tan 40 / (tan 40 + tan 35)