標題:

Secondary 3 mathematics problem(2)

發問:

Someone measures the angle of elevation of the top of the building from point A ,which is 58.2*.He then walks a distance of 108.3m to point B and finds that the angle of elevation is now 40.9*.Find the height of the building. THX!!!!!!!!!!!!!!!!

最佳解答:

let the height of the building be h, let the distance from point A to the building be x tan 58.2 = h / x x = h / 1.6128349 tan 40.9 = h / (x + 108.3) 0.8662271 = h / [(h / 1.6128349) + 108.3] 0.8662271[(h / 1.6128349) + 108.3] = h 0.53708355h+93. 812395 = h h = 202.66514m

其他解答:

aa.jpg

 

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http://flypicture.com/display/MTkzNjQz 圖片顯示A,B,x,y 的位置 Let the height of the building be y m Let the distant between A and the building be x m y tan 58.2* =---.................(1) x y tan 40.9*= ------------.................(2) (x+108.3) From (1),we have x tan 58.2* = y.................(3) Put (3) into (2), x tan 58.2* tan 40.9*= ------------ (x+108.3) x tan 40.9*+ 108.3 tan 40.9* =x tan 58.2* 108.3 tan 40.9* =x tan 58.2* - x tan 40.9* x =126 ( 3 s.f ) Put x =126 into (3) y = 202.7 so, the height of the building is 202.7 m
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