Cambridge International Mathematics

334 Trigonometry (Chapter 15)

a The projection of AH onto the base plane EFGH is EH

) the required angle is AHE.b

b The projection of AG onto the base plane EFGH is EG

) the required angle is AGE.b

Example 14 Self Tutor

Find the angle between the following line segments

and the base plane EFGH:

a DG b BH

EXERCISE 15F.2

1 Find the following projections onto the base planes of the given figures:

aiCF

ii DG

iii DF

iv CM

biPA

ii PN

ciBD

ii AE

iii AF

iv AX

H

G

E F

D C

A B

H G

E F

D C

A B

4cm

5cm

6cm

H

G

F

D C

A B

5cm

6cm

4cm E

q

H

G

E F

M

D C

A B

EXF

C

A B

D

AD

M

B

C

P

N

HG

F

5cm

6cm

E

H

G

F

D

A B

4cm

5cm

6cm

E

C

a

a The required angle is DGH.b

) tanμ=

OPP

ADJ

=^46

) μ= tan¡^1

¡ 4

6

¢

) μ¼ 33 : 69 o

) the angle is about 33 : 7 o

b The required angle is BbHF.

By Pythagoras,

(HF)^2 =6^2 +5^2

) (HF)^2 =61

) HF=

p

61 cm

tan®=

OPP

ADJ

=p^461

) ®= tan¡^1

³

p^4

61

́

) ®¼ 27 : 12 o

) the angle is about 27 : 1 o.

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Y:\HAESE\IGCSE01\IG01_15\334IGCSE01_15.CDR Tuesday, 7 October 2008 2:23:10 PM PETER