Maths 問題 (急)(10點)

2007-09-02 3:53 am

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A 長方形衣櫃 ABCD leans against the 角落 BOA of two perpendicular 牆如圖. AB = 120 cm, BC = 45 cm and ∠ABO = Θ.
(a) If Θ =60∘,
(i) 找出 point D 及 the wall OA 的距離, correct to 3位有效數字;
(ii) .......及 the wall OB, correct to 3 位有效數字.

(b) Find the measure of Θ 令point D 同埋 the wall OB 的距離最大. 搵埋 this largest distance, correct to 3位有效數字.

更新1:

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更新2:

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回答 (1)

wmheric

2007-09-02 8:03 pm

✔ 最佳答案

我估到少少幅圖係點...

(a)(i)
Let M be a point on the wall OA such that DM⊥OM.
[∠OAB = 180° - 90° - 60° = 30°
∠MAD = 180° - 90° - 30° = 60°]
The perpendicular distance from D to OA
= DM
= AD sin 60°
= 45 sin 60°
= 39.0 cm
(ii) Let N be a point on the wall OB such that DN⊥ON.
The perpendicular distance from D to OB
= DN
= MO
= MA + AO
= AD cos 60° + AB sin 60°
= 45 cos 60° + 120 sin 60°
= 126 cm

(b)
The required distance
= 45 cos θ + 120 sin θ
= R cos (θ - α) where R = √(45^2 + 120^2) = 15√73, tan α = 120/45 = 8/3
= R cos (θ - α)
For maximum required distance, cos (θ - α) = 1
θ - α = 0
θ = α = arctan (8/3) = 69.4°

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