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標題:
1math question
發問:
the angles of depression of point A and B from the top of a buildingCD are 30 degree and 48 degree respectively. If A and B lie on the same plane and are 150m apart, find the height of the building correct to 4 sig.fig. 唔該.
最佳解答:
Draw a diagram such that A, B and D are on the horizontal ground. C is the top of the building. Let BD = x m and CD = h m ∠CAD = 30 degree and ∠CBD = 48 degree In rt∠△ADC, tan∠CAD = h / ( x + 150 ) tan 30 degree = h / ( x + 150 ) x + 150 = h / tan 30 degree x = h / tan 30 degree – 150 . . . . . (1) In rt∠△BDC, tan∠CBD = h / x tan 48 degree = h / x x = h / tan 48 degree . . . . . . . . . . (2) Compare (1) and (2) : h / tan 30 degree – 150 = h / tan 48 degree 1.73205 h – 150 = 0.90040 h 0.83165 h = 150 h = 180.36 The height of the building is 180.4 m ( correct to 4 sig.fig. )
其他解答:
1math question
發問:
the angles of depression of point A and B from the top of a buildingCD are 30 degree and 48 degree respectively. If A and B lie on the same plane and are 150m apart, find the height of the building correct to 4 sig.fig. 唔該.
最佳解答:
Draw a diagram such that A, B and D are on the horizontal ground. C is the top of the building. Let BD = x m and CD = h m ∠CAD = 30 degree and ∠CBD = 48 degree In rt∠△ADC, tan∠CAD = h / ( x + 150 ) tan 30 degree = h / ( x + 150 ) x + 150 = h / tan 30 degree x = h / tan 30 degree – 150 . . . . . (1) In rt∠△BDC, tan∠CBD = h / x tan 48 degree = h / x x = h / tan 48 degree . . . . . . . . . . (2) Compare (1) and (2) : h / tan 30 degree – 150 = h / tan 48 degree 1.73205 h – 150 = 0.90040 h 0.83165 h = 150 h = 180.36 The height of the building is 180.4 m ( correct to 4 sig.fig. )
其他解答:
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