Box 1

1
Box 1
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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.
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)
13.3 cm (1 dp)
? angle FHB 13o
13 cm
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Wedge 1
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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)
11.1 m (1 dp)
? angle CEB 16.2o
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Box 2
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Trigonometry 3D Problems
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)
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)
25.5 cm (1 dp)
? angle AGE 11.3o
25 cm
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Wedge 2
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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)
11.8 m (1 dp)
? angle AFD 24.1o
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Flag pole 1
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)
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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
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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
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Q
O
42o
13m
R
T
24 m
10 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
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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
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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
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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
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Q
O
R
T
50o
10.77m
20 m
8 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
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Worksheets
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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
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
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
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.