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A. B. D. F. E. C. H. G. NOT TO SCALE. Trigonometry : 3D Problems. Example Question 1 : The diagram below shows a rectangular box with top ABCD and base EFGH. The distances are as indicated on the diagram. From the diagram find: (a) The distance BH (b) The angle FHB. Box 1. 3 cm.

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  1. A B D F E C H G NOT TO SCALE Trigonometry : 3D Problems Example Question1: The diagram below shows a rectangular box with top ABCD and base EFGH. The distances are as indicated on the diagram. From the diagram find: (a) The distance BH (b) The angle FHB. Box 1 3 cm 13 .3 cm 13 cm 5 cm 12 cm Find FH first then find BH. (a) FH2 = 122 + 52 (Pythag) BH2 = 132 + 32 (Pythag) (b) From triangle FHB tan FHB = 3/13 FH = (122 + 52) BH = (132 + 32)  angle FHB = 13o = 13.3 cm (1 dp) = 13 cm

  2. Wedge 1 A D B 3.1 m C E 5.4 m 9.2 m F NOT TO SCALE Trigonometry : 3D Problems Example Question 2: The diagram below shows a wedge in which rectangle ABCD is perpendicular to rectangle CDEF. The distances are as indicated on the diagram. From the diagram find: (a) The distance BE (to 1 dp) (b) The angle CEB (to 1 dp) Find EC first then find BE. (a) EC2 = 5.42 + 9.22 (Pythag) EC = (5.42 + 9.22) 11.1 m = 10.67 m 10 .67 m BE2 = 10.672 + 3.12 (Pythag) (b) From triangle CEB tan CEB = 3.1/10.67 BE = (10.672 + 3.12)  angle CEB = 16.2o = 11.1 m (1 dp)

  3. A B D F E C H G NOT TO SCALE Trigonometry : 3D Problems Question1: The diagram below shows a rectangular box with top ABCD and base EFGH. The distances are as indicated on the diagram. From the diagram find: (a) The distance AG (b) The angle EGA (to 1 dp) Box 2 5 cm 25.5 cm 25 cm 7 cm 24 cm Find EG first then find AG. (a) EG2 = 242 + 72 (Pythag) AG2 = 252 + 52 (Pythag) (b) From triangle AGE tan AGE = 5/25 EG = (242 + 72) AG = (252 + 52)  angle AGE = 11.3o = 25.5 cm (1 dp) = 25 cm

  4. Wedge 2 A D B 4.8 m C E 6.3 m 8.7 m F NOT TO SCALE Trigonometry : 3D Problems Question 2: The diagram below shows a wedge in which rectangle ABCD is perpendicular to rectangle CDEF. The distances are as indicated on the diagram. From the diagram find: (a) The distance AF (to 1 dp) (b) The angle DFA. (1 dp) Find DF first then find AF. (a) DF2 = 8.72 + 6.32 (Pythag) 10 .74 m DF = (8.72 + 6.32) 11.8 m = 10.74 m AF2 = 10.742 + 4.82 (Pythag) (b) From triangle AFD tan AFD = 4.8/10.74 AF = (10.742 + 4.82)  angle AFD = 24.1o = 11.8 m (1 dp)

  5. Flag pole 1 P Q 34o R T 15 m 30 m S Example Question 3: A vertical flag pole TP stands in the corner of a horizontal field QRST. Using the information given in the diagram, calculate (a) The height of the flag pole ( 1 dp) (b) The angle of elevation of P from S. (nearest degree) NOT TO SCALE 20.2 m (a) tan 34o = PT/30 (b) tan PST = 20.2/15  PT = 30 x tan34o  angle PST = 53o(nearest degree) = 20.2 m

  6. Pyramid 1 Example Question 4: A vertical flag pole OP stands in the centre of a horizontal field QRST. Using the information given in the diagram, calculate the height of the flag pole. P NOT TO SCALE Q O 42o 13m R T 10 m 24 m S TR2 = 102 + 242 (Pythag) tan 42o = OP/13 TR = (102 + 242)  OP = 13 x tan 42o = 11.7 m (1 dp) = 26 m TO =13 m

  7. Flagpole 2 Question 3: A vertical flag pole RP stands in the corner of a horizontal field QRST. Using the information given in the diagram, calculate (a) The height of the flag pole. (b) The angle of elevation of P from Q. P NOT TO SCALE Q 14 m 20 m R T 35o 9 m S (a) tan 35o = PR/20 (b) Tan RQP = 14/9  PR = 20 x tan35o  angle RQP = 57o(nearest degree) = 14 m

  8. Pyramid 2 Question 4: A vertical flag pole OP stands in the centre of a horizontal field QRST. Using the information given in the diagram, calculate the height of the flag pole. P NOT TO SCALE Q O R T 50o 10.77m 8 m 20 m S SQ2 = 82 + 202 (Pythag) tan 50o = OP/10.77 SQ = (82 + 202)  OP = 10.77 x tan 50o = 12.8 m (1 dp) = 21.54 m SO =10.77 m

  9. Worksheets Example Question 1: The diagram below shows a rectangular box with top ABCD and base EFGH. The distances are as indicated on the diagram. From the diagram find: (a) The distance BH (b) The angle FHB. 3 cm A B D 5 cm F E C 12 cm H G

  10. Example Question 2: The diagram below shows a wedge in which rectangle ABCD is perpendicular to rectangle CDEF. The distances are as indicated on the diagram. From the diagram find: (a) The distance BE (to 1 dp) (B) The angle CEB. A D B 3.1 m C E 5.4 m 9.2 m F

  11. Question 1: The diagram below shows a rectangular box with top ABCD and base EFGH. The distances are as indicated on the diagram. From the diagram find: (a) The distance AG (B) The angle EGA. 5 cm A B D 7 cm F E C 24 cm H G

  12. Question 2: The diagram below shows a wedge in which rectangle ABCD is perpendicular to rectangle CDEF. The distances are as indicated on the diagram. From the diagram find: (a) The distance AF (to 1 dp) (B) The angle DFA. A D B 4.8 m C E 6.3 m 8.7 m F

  13. P Q 34o R T 15 m 30 m S Example Question 3: A vertical flag pole TP stands in the corner of a horizontal field QRST. Using the information given in the diagram, calculate (a) The height of the flag pole. (b) The angle of elevation of P from S.

  14. P Q O 42o R T 10 m 24 m S Example Question 4: A vertical flag pole OP stands in the centre of a horizontal field QRST. Using the information given in the diagram, calculate the height of the flag pole.

  15. P Q 20 m R T 35o 9 m S Question 3: A vertical flag pole RP stands in the corner of a horizontal field QRST. Using the information given in the diagram, calculate (a) The height of the flag pole. (b) The angle of elevation of P from Q.

  16. P Q O R T 50o 8 m 20 m S Question 4: A vertical flag pole OP stands in the centre of a horizontal field QRST. Using the information given in the diagram, calculate the height of the flag pole.

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