標題:
F3 Maths (about the application of trigonometry)
發問:
1.From the deck of a boat, the angle of elevation of a helicopter is 53 degrees. From the top of the mast which is 10 m above the deck, the angle of elevation of the helicopter is 44 degrees. How high is the helicopter from the deck?2.From half-wayup a lighthouse, the angle of depression of a boat is 23... 顯示更多 1.From the deck of a boat, the angle of elevation of a helicopter is 53 degrees. From the top of the mast which is 10 m above the deck, the angle of elevation of the helicopter is 44 degrees. How high is the helicopter from the deck? 2.From half-wayup a lighthouse, the angle of depression of a boat is 23 degree .What will the angle of depression be of the same boat from the top of the light house ? please give detailed explanation and you may use figures to illustrate, please be reminded that clear solving process is also needed.
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最佳解答:
(1) Let y be the high of the helicopter from the deck of the boat and x be the horizontal distance from the helicopter to the boat y/ x = tan 53 --------(1) (y-10)/x = tan 44 ---------(2) sub (1) into (2): (y-10)(tan53/y) = tan44 ytan 53 - 10tan53 = ytan44 y = 10 tan53 / (tan53 - tan 44 = 36.7m (from the deck of boat) (2) Let high of the lighthouse be y and let the horizontal distance from the lighthosue to the boat be x, let the angle of depression for the boat to the lighthouse be a y/x = tan a 0.5y/x = tan23 tan a = 2 tan 23 a = 40.3
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