Cambridge International Mathematics

374 Similarity (Chapter 18)

Example 6 Self Tutor

When a 30 cm ruler is stood vertically on the ground it casts a 24 cm shadow.

At the same time a man casts a shadow of length 152 cm. How tall is the man?

The triangles are equiangular and)similar.

)

h

30

=

152

24

fsame ratiog

) h=

152

24

£ 30

) h= 190 i.e., the man is 190 cm tall.

® 90 ¡® 90

30 cm 24 cm - small 4

hcm 152 cm - large 4

EXERCISE 18C

1 Find the height of the pine tree:

ab

2 A ramp is built to enable wheelchair access to a building that is 24 cm above ground level. The ramp

has a constant slope of 2 in 15 , which means that for every 15 cm horizontally it rises 2 cm. Calculate

the length of the base of the ramp.

3 A piece of timber leaning against a wall, just touches

the top of a fence, as shown. Find how far up the wall

the timber reaches.

24 cm

30 cm

90 - a

a

152 cm

hcm

a

90 - a

1m

1.2 m 7.2 m

shadow

stick

1m

2.4 m 15.6 m

shadow

stick

building

15 cm

ground level

24 cm

2cm

timber

fence

1.6 m

3m 2m

wall

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y:\HAESE\IGCSE01\IG01_18\374IGCSE01_18.CDR Friday, 3 October 2008 12:57:14 PM PETER