maths problem

[匿名]

2014-01-02 6:44 am

1)In the figure, AOG is a straight line and angle AOB=angleBOC=angleCOD=angleDOE=angleEOF=angleFOG.If AG=7,find OD correct to 4 significant figures.
picture:http://postimg.org/image/5huznyf5r/
NEED STEP,PLZ!!!

回答 (1)

賣女孩的火柴

2014-01-02 7:38 am

✔ 最佳答案

Let ∠AOB = ∠BOC = ∠COD = ∠DOE = ∠EOF = ∠FOG = θ

∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOF + ∠FOG = 180°
6θ = 180°
θ = 30°

In ΔCOD :
cosθ = OD/OC
OC = OD/cos30°

In ΔBOC :
cosθ = OC/OB
OB = OC/cos30° = (OD/cos30°)/cos30° = OD/cos²30°

In ΔAOB :
cosθ = OB/OA
OA = OB/cos30° = (OD/cos²30°)/cos30° = OD/cos³30° = (8/3√3)OD

In ΔDOE :
cosθ = OE/OD
OE = OD cos30°

In ΔEOF :
cosθ = OF/OE
OF = OE cos30° = (OD cos30°) cos30° = OD cos²30°

In ΔFOG :
cosθ = OG/OF
OG = OF cos30° = (OD cos²30°) cos30° = OD cos³30° = (3√3/8)OD

AG = 7
OA + OG = 7
(8/3√3)OD + (3√3/8)OD = 7
OD = 7 ÷ [(8/3√3) + (3√3/8)]
OD = 3.198 (to 4 sig.fig.)

參考: 賣女孩的火柴

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