Question

如图,身高1.6m的小明从距路灯底部O点20m的A点沿OA所在直线行走了14m到B点时，身影的长度变短了3.5m

如图,身高1.6m的小明从距路灯底部O点20m的A点沿OA所在直线行走了14m到B点时，身影的长度变短了3.5m，求路灯P距离地面个高度

Answer 1

如图，AC=BD = 1.6, AM-BN = 3.5

AB = 14, OB = 6

设OP = h, BN = x, AM = x + 3.5

h/(OB+BN) = DB/BN => h/(6+x) = 1.6/x

h/(OA+AM) = AC/AM => h/(20+x+3.5) = 1.6 / (x+3.5)

hx = 9.6 + 1.6x

 

hx + 3.5h = 37.6 + 1.6x

9.6 + 1.6x + 3.5h = 37.6 + 1.6x

h = (37.6 - 9.6)/3.5 = 8m

Answer 2