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Figure: http://img192.imageshack.us/f/img192/3414/89124776.pngIn the figure, OT is a lighthouse of height 250 m. O, A and B are on the same horizontal ground. AB is a straight road of length 310 m. The angle of elevation of the top T of the lighthouse form A and B are 48 and 62 respectively.a) Find AT and... 顯示更多 Figure: http://img192.imageshack.us/f/img192/3414/89124776.png In the figure, OT is a lighthouse of height 250 m. O, A and B are on the same horizontal ground. AB is a straight road of length 310 m. The angle of elevation of the top T of the lighthouse form A and B are 48 and 62 respectively. a) Find AT and BT. Ans: AT = 336 m, BT = 283 m b) Find angle TAB. ans: 51.8 c) Find the angle between the plane ABT and the horizontal ground. Ans: 71.1 d) When a small object P moves along AB, is it possible that the angle of elevation of T form P at a certain point on AB is 78 degree. Explain your ans: no
最佳解答:
圖片參考：http://img192.imageshack.us/img192/3414/89124776.png a) AT = 250 / sin48 = 336.40818 = 336 m BT = 250 / sin62 = 283.14251 = 283 m b) CosㄥTAB = (AT^2 + AB^2 - BT^2) / (2 AT AB) CosㄥTAB = (336.40818^2 + 310^2 - 283.14251^2) / (2 * 336.40818 * 310) CosㄥTAB = 0.61897 ㄥTAB = 51.7589 = 51.8° c) Let X be a point on AB such that OX 丄 AB , the required angle = ㄥTXO , The area of △TAB = (1/2) AT * AB sinㄥTAB = (1/2)AB * TX 336.40818 * 310 * sin 51.7589 = 310 TX TX = 264.22 sin ㄥTXO = TO/TX = 250 / 264.22 ㄥTXO = 71.117 = 71.1° d) No. sin ㄥTPO = TO / TP , since the largest length of TP = TX , hence sin ㄥTPO = TO/TP =< TO/TX = 250/264.22, ㄥTPO =< 71.1° , 78° is impossible. 2010-05-26 19:36:45 補充： It should be the smallest length of TP = TX , hence sin ㄥTPO = TO/TP >= TO/TX = 250/264.22, ㄥTPO =< 71.1° , 78° is impossible.
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SS1 Maths 3-D problems ...發問:
Figure: http://img192.imageshack.us/f/img192/3414/89124776.pngIn the figure, OT is a lighthouse of height 250 m. O, A and B are on the same horizontal ground. AB is a straight road of length 310 m. The angle of elevation of the top T of the lighthouse form A and B are 48 and 62 respectively.a) Find AT and... 顯示更多 Figure: http://img192.imageshack.us/f/img192/3414/89124776.png In the figure, OT is a lighthouse of height 250 m. O, A and B are on the same horizontal ground. AB is a straight road of length 310 m. The angle of elevation of the top T of the lighthouse form A and B are 48 and 62 respectively. a) Find AT and BT. Ans: AT = 336 m, BT = 283 m b) Find angle TAB. ans: 51.8 c) Find the angle between the plane ABT and the horizontal ground. Ans: 71.1 d) When a small object P moves along AB, is it possible that the angle of elevation of T form P at a certain point on AB is 78 degree. Explain your ans: no
最佳解答:
圖片參考：http://img192.imageshack.us/img192/3414/89124776.png a) AT = 250 / sin48 = 336.40818 = 336 m BT = 250 / sin62 = 283.14251 = 283 m b) CosㄥTAB = (AT^2 + AB^2 - BT^2) / (2 AT AB) CosㄥTAB = (336.40818^2 + 310^2 - 283.14251^2) / (2 * 336.40818 * 310) CosㄥTAB = 0.61897 ㄥTAB = 51.7589 = 51.8° c) Let X be a point on AB such that OX 丄 AB , the required angle = ㄥTXO , The area of △TAB = (1/2) AT * AB sinㄥTAB = (1/2)AB * TX 336.40818 * 310 * sin 51.7589 = 310 TX TX = 264.22 sin ㄥTXO = TO/TX = 250 / 264.22 ㄥTXO = 71.117 = 71.1° d) No. sin ㄥTPO = TO / TP , since the largest length of TP = TX , hence sin ㄥTPO = TO/TP =< TO/TX = 250/264.22, ㄥTPO =< 71.1° , 78° is impossible. 2010-05-26 19:36:45 補充： It should be the smallest length of TP = TX , hence sin ㄥTPO = TO/TP >= TO/TX = 250/264.22, ㄥTPO =< 71.1° , 78° is impossible.
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