Question

如图①，南京中山陵的台阶拾级而上被分成坡度不等的两部分．图②是台阶的侧面图，若斜坡BC长为120 m，在C处看B处的仰角为25°；斜坡AB长70 m，在A处看B处的俯角为50°，试求出陵墓的垂直高度AE的长．

（参考数据：sin50°≈0.77，cos50°≈0.64，tan50°≈1.19，sin25°≈0.42，cos25°≈0.91，tan25°≈0.47）

	图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的长为104.3 m．······················································· 8分