Mathematics_1－wszspj2的部落格

標題:

Mathematics

發問:

圖片參考：http://imgcld.yimg.com/8/n/HA00037652/o/701204080054013873390980.jpg -============================================================

最佳解答:

ai) OB2 = 3002 + 1002 - 2*300*100 cos(90 - 30)° OB2 = 100000 - 30000 OB = 100√7 maii) tan∠TAO = TO / 300 tan∠TAO = OB tan35° / 300 tan∠TAO = 100√7 tan35° / 300 tan∠TAO = 0.61753 ∠TAO = 31.69637 = 32°(nearest degree) b) BC = 300 - 100sin30° = 250 m ci) sin∠OBA / 300 = sin∠OAB / OB sin∠OBA / 300 = sin60° / (100√7) sin∠OBA = (3/2)√(3/7) (BD/2) / OB = sin∠OBA (BD/2) / (100√7) = (3/2)√(3/7) BD = 300√3 AD = BD - BA = 300√3 - 100 = 420 m (3 sig. fig.) cii) By ci) , sin∠OBA = (3/2)√(3/7) ∠OBA = 79.1°∠OBC = 180° - 79.1° - 60° = 40.9° So ∠OBA > ∠OBC , then BD < BE , Peter route is shorter.