Box 1

A B

FC

GH

D E

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.

Trigonometry : 3D Problems

12 cm

5 cm

(a) FH2 = 122 + 52 (Pythag)

FH = (122 + 52)

= 13 cm

BH2 = 132 + 32 (Pythag)

BH = (132 + 32)

= 13.3 cm (1 dp)

tan FHB = 3/13

angle FHB = 13o

Find FH first then find BH.

13 cm

13 .3 cm

(b) From triangle FHB

3 cm

NOT TO SCALE

Wedge 1

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)

Trigonometry : 3D Problems

A

B

C

D

E

F

5.4 m 9.2 m

3.1 m

(a) EC2 = 5.42 + 9.22 (Pythag)

EC = (5.42 + 9.22)

= 10.67 m

BE2 = 10.672 + 3.12 (Pythag)

BE = (10.672 + 3.12)

= 11.1 m (1 dp)

tan CEB = 3.1/10.67

angle CEB = 16.2o

Find EC first then find BE.

(b) From triangle CEB

10 .67 m

11.1 m

NOT TO SCALE

Box 2

A B

FC

GH

D E

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)

Trigonometry : 3D Problems

24 cm

7 cm

(a) EG2 = 242 + 72 (Pythag)

EG = (242 + 72)

= 25 cm

AG2 = 252 + 52 (Pythag)

AG = (252 + 52)

= 25.5 cm (1 dp)

tan AGE = 5/25

angle AGE = 11.3o

Find EG first then find AG.

25 cm

25.5 cm

(b) From triangle AGE

5 cm

NOT TO SCALE

Wedge 2

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)

Trigonometry : 3D Problems

A

B

C

D

E

F

6.3 m 8.7 m

4.8 m

(a) DF2 = 8.72 + 6.32 (Pythag)

DF = (8.72 + 6.32)

= 10.74 m

AF2 = 10.742 + 4.82 (Pythag)

AF = (10.742 + 4.82)

= 11.8 m (1 dp)

tan AFD = 4.8/10.74

angle AFD = 24.1o

Find DF first then find AF.

(b) From triangle AFD

10 .74 m

11.8 m

NOT TO SCALE

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)

Q

30 m

34o

15 m

TR

P

S(a) tan 34o = PT/30

PT = 30 x tan34o

= 20.2 m

(b) tan PST = 20.2/15

angle PST = 53o (nearest degree)

20.2 m

NOT TO SCALE

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.

24 m10 m

Q

O

P

T

tan 42o = OP/13

OP = 13 x tan 42o = 11.7 m (1 dp)

13m R

TR2 = 102 + 242 (Pythag)

TR = (102 + 242)

= 26 m TO = 13 m

S

42o

NOT TO SCALE

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.

Q

20 m

9 m

TR

P

S

(a) tan 35o = PR/20

PR = 20 x tan35o

= 14 m

(b) Tan RQP = 14/9

angle RQP = 57o (nearest degree)

14 m

35o

NOT TO SCALE

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.

20 m8 m

Q

O

P

T

tan 50o = OP/10.77

OP = 10.77 x tan 50o = 12.8 m (1 dp)

10.77m

R

SQ2 = 82 + 202 (Pythag)

SQ = (82 + 202)

= 21.54 m SO = 10.77 m

S

50o

NOT TO SCALE

Worksheets

A B

FC

GH

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.

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

FC

GH

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.

Q

30 m

34o

15 m

TR

P

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.

24 m10 m

Q

O

P

T R

S

42o

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.

Q

20 m

9 m

TR

P

S

35o

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.

20 m8 m

Q

O

P

T R

S

50o

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.