1 / 16

Box 1

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.

jamil
Télécharger la présentation

Box 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related