3D applications of trigonometry HKCEE Paper 1 past paper sorted by topic ( )
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1 3D applications of trigonometry HKCEE Paper 1 past paper sorted by topic ( ) Vertical pole 鉛垂柱 Solid figures 立體 Shadow 影子 Paper folding 摺紙 Inclined plane 斜面 1980 X 1981 NA 1982 X 1983 X 1984 X 1985 X 1986 X 1987 X 1988 X 1989 X 1990 X 1991 NA 1992 X 1993 X 1994 X 1995 X 1996 X 1997 NA 1998 X 1999 X 2000 Laser projection on vertical wall 激光投射 2001 X 2002 X 2003 X 2004 X 2005 X 2006 X 2007 X 2008 X 2009 X Page 1
2 Vertical pole on horizontal triangular plane 1980B9 P h NORTH WEST α x C y β EAST A SOUTH 400 B In the figure, PC represents a vertical object of height h metres. From a point A, south of C, the angle of elevation of P is α. From a point B, 400 metres east of A, the angle of elevation of P is β. AC and BC are x metres and y metres respectively. (a) (i) Express x in terms of h and α. (ii) Express y in terms of h and β. (4 marks) (b) If = 60 α and β = 30, find the value of h correct to 3 significant figures. (6 marks) Page 2
3 1983B13 H 50 m 30 C 45 A EAST P B SOUTH In the figure, A, B and C are three points on the same horizontal ground. HC is a vertical tower 50 m high. A and B are respectively due east and due south of the tower. The angles of elevation of H observed from A and B are respectively 45 and 30. (a) Find the distance between A and B. (6 marks) (b) P is a point on AB such that CP AB. (i) (ii) Find the distance between C and P to the nearest metre. Find the angle of elevation of H observed from P to the nearest degree. (6 marks) Page 3
4 1984B13 Page 4
5 1985B8 Page 5
6 1986B10 Page 6
7 1990B10 Page 7
8 1993B12 Page 8
9 1994B14 Page 9
10 2002B14 Page 10
11 2008B15 Page 11
12 Solid figures 1982B8 B y cm 9 cm x cm C A x cm Figure not drawn to scale The figure represents the framework of a cuboid made of iron wire. It has a square base of side x cm and a height of y cm. The length of the diagonal AB is 9 cm. The total length of wire used for the framework (including the diagonal AB) is 69 cm. (a) Find all the values of x and y. (10 marks) (b) Hence calculate ABC to the nearest degree for the case in which y > x. (2 marks) Page 12
13 1987B11 Page 13
14 2005B14 Page 14
15 2007B16 Page 15
16 2009B17 The figure shows a geometric model fixed on the horizontal ground. The model consists of two thin triangular metal plates ABE and CDE, where D lies on AB and CE is perpendicular to the thin metal plate ABE. It is given that A, B, C and D lie on the horizontal ground. It is found that AC = 28 cm, BC = 25 cm, BD = 6 cm, BE = 24 cm and ABC = 57. E A D C B (a) Find (i) the length of CD, (ii) BAC, (iii) the area of ABC, (iv) the shortest distance from E to the horizontal ground. (9 marks) (b) A student claims that the angle between DE and the horizontal ground is CDE. Do you agree? Explain your answer. (2 marks) Page 16
17 Plane object under sunshine and its shadow 1988B13 Page 17
18 1989B10 Figure 3 Page 18
19 1995B15 Page 19
20 1998B17 Page 20
21 2003B14 Page 21
22 Paper Folding 1992B15 Figure 8a Page 22
23 1999B18 Page 23
24 2001B16 Page 24
25 2006B17 In Figure 1, ABC is a triangular paper card. D is a point lying on AC such that BD is perpendicular to AC. It is known that AB = 40cm, BC = 60cm and AC = 90cm. B 60 cm C 40 cm D 90 cm A (a) Find AD. Figure 1 (2 marks) (b) The triangular paper card in the figure is folded along BD such that AB and BC lie on a horizontal plane as shown in Figure 2. D B C A Figure 2 (i) Suppose DAC = 62. (1) Find the distance between A and C on the horizontal plane. (2) Using Heron s formula, or otherwise, find the area of ABC on the horizontal plane. (3) Find the height of the tetrahedron ABCD from the vertex D to the base ABC. (ii) Describe how the volume of the tetrahedron ABCD varies when ADC increases from 30 to 150. Explain your answer. (9 marks) Page 25
26 Rectangular inclined plane 1996B15 Page 26
27 2004B17 Page 27
28 Laser projection 2000B17 Page 28
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