Question

如圖①，南京中山陵的臺階拾級而上被分成坡度不等的兩部分．圖②是臺階的側(cè)面圖，若斜坡BC長為120 m，在C處看B處的仰角為25°；斜坡AB長70 m，在A處看B處的俯角為50°，試求出陵墓的垂直高度AE的長．

（參考數(shù)據(jù)：sin50°≈0.77，cos50°≈0.64，tan50°≈1.19，sin25°≈0.42，cos25°≈0.91，tan25°≈0.47）

	圖①

Answer 1

解：在Rt△BDC中，sinC＝，········································································· 1分

∴BD＝BC·sinC＝BC·sin25°＝120×0.42＝50.4 m．··································· 3分

在Rt△AFB中，sin∠ABF＝，································································· 4分

∴AF＝AB·sin∠ABF＝AB·sin50°＝70×0.77＝53.9 m．····························· 6分

∴AE＝AF＋FE＝AF＋BD＝50.4＋53.9＝104.3 m．

答：陵墓的垂直高度AE的長為104.3 m．······················································· 8分