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Trigonometry : 3 D Problems NOT TO SCALE Example Question 1: The diagram below Trigonometry : 3 D Problems NOT TO SCALE 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. A B 3 cm 13. 3 cm D E F C 13 cm H Find FH first then find BH. (a) FH 2 = 122 + 52 (Pythag) FH = (122 + 52) = 13 cm 12 cm 5 cm G BH 2 = 132 + 32 (Pythag) BH = (132 + 32) = 13. 3 cm (1 dp) Box 1 (b) From triangle FHB tan FHB = 3/13 angle FHB = 13 o

Trigonometry : 3 D Problems NOT TO SCALE Example Question 2: The diagram below Trigonometry : 3 D Problems NOT TO SCALE 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) A Find EC first then find BE. D (a) EC 2 = 5. 42 + 9. 22 (Pythag) EC = (5. 42 + 9. 22) = 10. 67 m 11. 1 m E 10. 67 m 5. 4 m F BE 2 = 10. 672 + 3. 12 (Pythag) BE = (10. 672 + 3. 12) = 11. 1 m (1 dp) Wedge 1 9. 2 m (b) From triangle CEB tan CEB = 3. 1/10. 67 angle CEB = 16. 2 o B 3. 1 m C

Trigonometry : 3 D Problems NOT TO SCALE Question 1: The diagram below shows Trigonometry : 3 D Problems NOT TO SCALE 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 (to 1 dp) A B 5 cm 25. 5 cm D E F C 25 cm H Find EG first then find AG. (a) EG 2 = 242 + 72 (Pythag) EG = (242 + 72) = 25 cm 24 cm 7 cm G AG 2 = 252 + 52 (Pythag) AG = (252 + 52) = 25. 5 cm (1 dp) (b) From triangle AGE tan AGE = 5/25 Box 2 angle AGE = 11. 3 o

Trigonometry : 3 D Problems NOT TO SCALE Question 2: The diagram below shows Trigonometry : 3 D Problems NOT TO SCALE 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) A Find DF first then find AF. D (a) DF 2 = 8. 72 + 6. 32 (Pythag) 10. 74 m DF = (8. 72 + 6. 32) = 10. 74 m 11. 8 m E 6. 3 m 8. 7 m F AF 2 = 10. 742 + 4. 82 (Pythag) AF = (10. 742 + 4. 82) = 11. 8 m (1 dp) (b) From triangle AFD tan AFD = 4. 8/10. 74 angle AFD = 24. 1 o Wedge 2 B 4. 8 m C

Example Question 3: A vertical flag pole TP stands in the corner of a 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) P NOT TO SCALE 34 o 20. 2 m Q R T 15 m (a) tan 34 o = PT/30 PT = 30 x tan 34 o = 20. 2 m 30 m S (b) tan PST = 20. 2/15 Flag pole 1 angle PST = 53 o (nearest degree)

Example Question 4: A vertical flag pole OP stands in the centre of a 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 T 42 o 13 m 10 m O R 24 m S TR 2 = 102 + 242 (Pythag) TR = (102 + 242) = 26 m TO = 13 m tan 42 o = OP/13 Pyramid 1 OP = 13 x tan 42 o = 11. 7 m (1 dp)

Question 3: A vertical flag pole RP stands in the corner of a horizontal 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 35 o 9 m S (a) tan 35 o = PR/20 PR = 20 x tan 35 o = 14 m (b) Tan RQP = 14/9 angle RQP = 57 o (nearest degree) Flagpole 2

Question 4: A vertical flag pole OP stands in the centre of a horizontal 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 T R 50 o 10. 77 m 8 m 20 m S SQ 2 = 82 + 202 (Pythag) SQ = (82 + 202) = 21. 54 m SO = 10. 77 m tan 50 o = OP/10. 77 Pyramid 2 OP = 10. 77 x tan 50 o = 12. 8 m (1 dp)

Example Question 1: The diagram below shows a rectangular box with top ABCD and 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. A B 3 cm D E F C 5 cm H 12 cm G Worksheets

Example Question 2: The diagram below shows a wedge in which rectangle ABCD is 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

Question 1: The diagram below shows a rectangular box with top ABCD and base 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. A B 5 cm D E F C 7 cm H 24 cm G

Question 2: The diagram below shows a wedge in which rectangle ABCD is perpendicular 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

Example Question 3: A vertical flag pole TP stands in the corner of a 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. P 34 o Q R T 15 m 30 m S

Example Question 4: A vertical flag pole OP stands in the centre of a 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 Q T O 42 o 10 m R 24 m S

Question 3: A vertical flag pole RP stands in the corner of a horizontal 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 Q 20 m R T 35 o 9 m S

Question 4: A vertical flag pole OP stands in the centre of a horizontal 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 Q O T R 50 o 8 m 20 m S