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Stair design of campus library
(1)∵ The height of steps is 0.3m,

∴ Height difference between point D and point C =6×0.3m= 1.8m,

∴ Height difference between point B and point A BH =1.8m;

So the answer is 1.8.

(2) In Rt△ABH, BH= 1.8, ∠ Bah = 34.2,

∴ sin34.2 = bhab ≈ 0.56, namely ab =1.80.56 ≈ 3.21(m),

∴ The total length of stainless steel material used is L = AC+AB+BD =1+3.21+1≈ 5.2 (m).

(3) As shown in the figure, the extension lines of BH and EF intersect at point M,

In Rt△ABH, BH= 1.8, ∠ bah = 34.2,

∴tan34.2 =BHAH=0.68,

∴AH= 1.80.68≈2.65(m),

In Rt△PDM, DM = BH+0.3 =1.8+0.3 = 2.1m, ∠ DPF = 15.

∴tan 15 =DMPM,

∴PM=2. 10.27≈7.78m,

∴pe=pm-em=am-ah=7.78-2.65≈5. 1(m),

That is, the slope occupies more than 5. 1m of the ground.