Cambridge International Mathematics

332 Trigonometry (Chapter 15)

Example 11 Self Tutor

A cube has sides of length 10 cm. Find the angle

between the diagonal AB of the cube and one of the

edges at B.

The angle between AB andanyof the edges at B is the same.

) the required angle is ABC.b

By Pythagoras:

x^2 =10^2 +10^2

) x^2 = 200

) x=

p

200

tanμ=

OPP

ADJ

=

p

200

10

) μ= tan¡^1

³p

200

10

́

) μ¼ 54 : 7 o The required angle is about 54 : 7 o:

EXERCISE 15F.1

1 The figure alongside is a cube with sides of length

15 cm. Find:

a EG b AGE.b

2 The figure alongside is a rectangular prism. X and Y are the

midpoints of the edges EF and FG respectively. Find:

a HX b DbXH c HY d DYH.b

3 In the triangular prism alongside, find:

a DF

b AbFD.

4 AB and BC are wooden support struts on a crate. Find the

total length of wood required to make the two struts.

A

C

xcm 10 cm

A

B

C

A

B

C

q

10

~` 2 ` 0 ` 0

A

B

C

q 10 cm

xcm

6cm

A

E

D

H

B

C

G

F 8cm

10 cm

X Y

4cm

3cm

A 8cm B

C

F

E

D

A B

D C

E

HG

F

A

B

C

25 cm

40° 35°

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Y:\HAESE\IGCSE01\IG01_15\332IGCSE01_15.CDR Thursday, 2 October 2008 9:39:46 AM PETER