Math topic中文

2d 3d problems

problems in two and three dimensions including those involving angles of elevation and depression and bearings

Practice questions

  1. 1The diagram shows the positions of a harbour, H, a lighthouse, L, and two buoys P and Q. HPQ is a straight line. The bea…
  2. 2In the diagram, PQRS is a vertical rectangular wall of height 2.5 m and length 7.5 m. T is a point on level ground from…
  3. 3The diagram shows four points P, Q, R and S which lie on level ground in a garden. P is due south of Q. The bearing of S…
  4. 4In the diagram, ABCDEFGH is a cuboid with dimensions 8 cm by 6 cm by 15 cm. V is the centre of the rectangular base. Sho…
  5. 5The figure above shows a solid. The cross-section of the solid is a sector of a circle of radius 5 cm and angle 30°. The…
  6. 6The diagram shows a parallelogram ABCD on horizontal ground where AC is a path. AB = 15 m and BC = 8 m. The bearing of B…
  7. 7The diagram above shows a park ABCDABCD that is on horizontal ground, crossed by a straight path ACAC. Point BB is due no…
  8. 8The diagram shows the positions of 3 points A, B, and C, at sea level. AB = 4.83 km and BC = 7.24 km. The bearing of B f…
  9. 9Airport B is 500 km away from airport A on a bearing of 064°. An aircraft leaves airport A at 22 45 on Monday to fly to…
  10. 10The diagram shows a goat tied to a pole at A. The length of the rope attached to the goat is 6 m. A is due west of the c…
  11. 11The diagram shows the positions of four checkpoints W, X, Y and Z in a jungle reserve area. The checkpoints are connecte…
  12. 12In the diagram, a wooden ramp is shown where ∠BCF=90∘\angle BCF = 90^\circ and ∠CBF=35∘\angle CBF = 35^\circ. ABCD, CDEF and ABFE ar…
  13. 13The diagram shows a rectangular table ABCD arranged such that the side AD is inclined at an angle of θ\theta to the wal…
  14. 14测量塔高ABAB时，选取与塔底BB在同一水平面内的两个测量点CC与DD，现测得∠BCD=5π12{\rm∠}BCD=\dfrac{5π}{12}，∠BDC=π3{\rm∠}BDC=\dfrac{π}{3}，CD=100CD=100，在点CC…
  15. 15An aircraft waiting to land is flying around a triangular circuit ABC. A, B and C are vertically above three beacons, X,…
  16. 16P, Q, R and S are four villages located on an island, where Q is due north of R. PQ = 924 m, QR = 640 m, PR = 1124 m, RS…
  17. 17The figure shows two rods PA and PB which are hinged at P. The rods slide such that P, A and B are on the same vertical…
  18. 18The diagram shows four points P, Q, R and S on level ground. Q is due east of P. Angle SPQ = 40° and angle PSR = 15°. PQ…
  19. 19O is the centre of the equilateral triangle. The triangle ABC forms the base of a pyramid. The vertex, X is vertically a…
  20. 20The diagram below shows an indoor adventure park in the shape of a trapezoidal prism with a square base ABCD. The indoor…
  21. 2122 P, Q and R are three points on level ground such that RPQ forms a right-angled triangle with PQ and RQ measuring 135…
  22. 22The diagram shows a lecture theatre in the shape of a prism with height 9 metres. The floor of the lecture theatre, ABCD…
  23. 23The diagram below shows three points, A, B and C on flat ground. AB = 80 m, AC = 100 m and BC = 90 m. C is due east of A…
  24. 24ABL is a park on horizontal ground. A is 1390 m from L on a bearing of 076°. B is 960 m from L on a bearing of 138°. Fin…
  25. 25A, B, C and D are points on horizontal ground. AB = 35 m and BC = 68 m. The bearing of B from A is 137∘137^\circ and the b…
  26. 26The diagram shows the positions of three towns, A, B and C. AB is 73 km, BC is 62 km and AC is 56 km. A is due North of…
  27. 27The diagram represents a flat plot of land PQRS. Find the area of the land PQRS. Answer ___ m^2 the length of PS. Answer…
  28. 28A container is a prism with a cross section in the shape of a right-angled triangle. The container has a height of 12 cm…
  29. 29The diagram shows a field ABCD on horizontal ground. Angle ABC = 115°, Angle CAD = 58°, AB = 9 m, BC = 6 m and CD = 11 m…
  30. 30Figure 1 shows an open container in the form of an isosceles trapezoidal prism ABCDEFGH with square base ABCD of sides xx…
  31. 31The diagram shows an accurate drawing of triangle ABC. By constructing appropriate lines on the diagram, mark the point…
  32. 32The diagram shows five towns A, B, C, D and E. Towns B, C, D lie on a straight line. Town E is due east of Town D. It is…
  33. 33On the scale drawing, P, Q, R and S are the positions of four garden statues in a park. PQRS is a quadrilateral. Scale:…
  34. 34Points A, B, C and D are at sea level. AD = 980 km, AB = 710 km and CD = 1100 km. The bearing of B and C from A are 148°…
  35. 35P, Q, R and S are points on a triangular garden. S R Q is a straight line. It is given that PQ=55 mPQ = 55\ \text{m}, RQ=40 mRQ = 40\ \text{m}…
  36. 36ABCD is a field on horizontal ground. AD = 168 m, BD = 325 m and CD = 151 m. The bearing of B from A is 155° and the bea…
  37. 3726 X, Y, and Z are three points on a horizontal sea level map as shown below. X is due North of Y and Z is due east of Y…
  38. 38The diagram shows part of a map of a small town. Joel's house is located at point W, the childcare centre at point X, th…
  39. 39ABCD is a field on horizontal ground. AD = 163 m, BD = 329 m, CD = 152 m and angle BDC = 48°. The bearing of B from A is…
  40. 40Three points A, B and C lie on a horizontal ground are such that AB = 24 m and BC = 53 m. Point B is due north of C. The…
  41. 41W, X, Y and Z are points on a horizontal ground and PW is a vertical flag pole. WX=7 mWX = 7\ \text{m}, WZ=3 mWZ = 3\ \text{m},…
  42. 42The diagram shows a cuboid with height x cm. The width of the cuboid is 6 cm more than its height. The length of the cub…
  43. 43A, B and C are three points on horizontal ground. The bearing of A from B is 040°. Find the bearing of B from A. Answer…
  44. 44The diagram shows the positions of points A, B and C. ∠ABC=60∘\angle ABC = 60^\circ, ∠BCA=54∘\angle BCA = 54^\circ and the bearing o…