Trigonometry : 3D 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 F C G H D E 3 cm 13 .3 cm 13 cm 5 cm Box 1 12 cm Find FH first then find BH. (a) FH2 = 122 + 52 (Pythag) BH2 = 132 + 32 (Pythag) (b) From triangle FHB FH = (122 + 52) BH = (132 + 32) tan FHB = 3/13 = 13 cm = 13.3 cm (1 dp)  angle FHB = 13o

Trigonometry : 3D 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 B C D E F 5.4 m 9.2 m 3.1 m 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 Wedge 1 BE2 = 10.672 + 3.12 (Pythag) (b) From triangle CEB BE = (10.672 + 3.12) tan CEB = 3.1/10.67 = 11.1 m (1 dp)  angle CEB = 16.2o

Trigonometry : 3D 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 F C G H D E 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 EG = (242 + 72) AG = (252 + 52) tan AGE = 5/25 Box 2 = 25 cm = 25.5 cm (1 dp)  angle AGE = 11.3o

Trigonometry : 3D 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 B C D E F 6.3 m 8.7 m 4.8 m Find DF first then find AF. (a) DF2 = 8.72 + 6.32 (Pythag) DF = (8.72 + 6.32) 10 .74 m 11.8 m = 10.74 m AF2 = 10.742 + 4.82 (Pythag) (b) From triangle AFD AF = (10.742 + 4.82) tan AFD = 4.8/10.74 Wedge 2 = 11.8 m (1 dp)  angle AFD = 24.1o

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) Q 30 m 34o 15 m T R P S NOT TO SCALE 20.2 m (a) tan 34o = PT/30 (b) tan PST = 20.2/15 Flag pole 1  PT = 30 x tan34o  angle PST = 53o (nearest degree) = 20.2 m

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 42o O 13m R T 10 m 24 m S TR2 = 102 + 242 (Pythag) tan 42o = OP/13 Pyramid 1 TR = (102 + 242)  OP = 13 x tan 42o = 11.7 m (1 dp) = 26 m TO = 13 m

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 Flagpole 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) Pyramid 2  OP = 10.77 x tan 50o = 12.8 m (1 dp) = 21.54 m SO = 10.77 m

A B F C G H D E 12 cm 5 cm 3 cm 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. Worksheets

A B C D E F 5.4 m 9.2 m 3.1 m 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 B F C G H D E 24 cm 7 cm 5 cm 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 C D E F 6.3 m 8.7 m 4.8 m 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.

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. Q 30 m 34o 15 m T R P 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. 24 m 10 m Q O P T R S 42o

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. Q 20 m 9 m T R P S 35o

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. 20 m 8 m Q O P T R S 50o