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
3 cm
13 .3 cm
D
E
F
C
13 cm
H
12 cm
5 cm
G
Find FH first then find BH.
(a) FH2 = 122 + 52 (Pythag)
FH = (122 + 52)
= 13 cm
BH2 = 132 + 32 (Pythag)
BH = (132 + 32)
= 13.3 cm (1 dp)
Box 1
(b) From triangle FHB
tan FHB = 3/13
 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
Find EC first then find BE.
D
(a) EC2 = 5.42 + 9.22 (Pythag)
EC = (5.42 + 9.22)
= 10.67 m
11.1 m
E
10 .67 m
5.4 m
9.2 m
F
BE2 = 10.672 + 3.12 (Pythag)
BE = (10.672 + 3.12)
= 11.1 m (1 dp)
Wedge 1
(b) From triangle CEB
tan CEB = 3.1/10.67
 angle CEB = 16.2o
B
3.1 m
C
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
5 cm
25.5 cm
D
E
F
C
25 cm
H
24 cm
7 cm
G
Find EG first then find AG.
(a) EG2 = 242 + 72 (Pythag)
EG = (242 + 72)
= 25 cm
AG2 = 252 + 52 (Pythag)
AG = (252 + 52)
= 25.5 cm (1 dp)
(b) From triangle AGE
tan AGE = 5/25
 angle AGE = 11.3o
Box 2
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
Find DF first then find AF.
D
(a) DF2 = 8.72 + 6.32 (Pythag)
DF = (8.72 + 6.32)
= 10.74 m
10 .74 m
11.8 m
E
6.3 m
8.7 m
F
AF2 = 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 = 24.1o
Wedge 2
B
4.8 m
C
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
34o
20.2 m
Q
R
T
15 m
(a) tan
34o
= PT/30
 PT = 30 x tan34o
= 20.2 m
30 m
S
(b) tan PST = 20.2/15
Flag pole 1
 angle PST = 53o (nearest degree)
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
42o
13m
10 m
O
R
24 m
S
TR2 = 102 + 242 (Pythag)
TR = (102 + 242)
= 26 m
TO = 13 m
tan 42o = OP/13
Pyramid 1
 OP = 13 x tan 42o = 11.7 m (1 dp)
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
9m
S
(a) tan 35o = PR/20
 PR = 20 x tan35o
= 14 m
(b) Tan RQP = 14/9
 angle RQP = 57o (nearest degree)
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
T
R
50o 10.77m
8m
20 m
S
SQ2 = 82 + 202 (Pythag)
SQ = (82 + 202)
= 21.54 m
SO = 10.77 m
tan 50o = OP/10.77
 OP = 10.77 x tan 50o = 12.8 m (1 dp)
Pyramid 2
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 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 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 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 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
34o
Q
R
T
15 m
30 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.
P
Q
T
O
42o
10 m
R
24 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.
P
Q
20 m
R
T
35o
9m
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.
P
Q
O
T
R
50o
8m
20 m
S