Cambridge International Mathematics

FINDING SIDES

Example 5 Self Tutor

Find the length of side BC correct

to 2 decimal places:

Using the sine rule:

BC

sin 113o

=

18

sin 41o

) BC=

18 £sin 113o

sin 41o

) BC¼ 25 : 26

) BC is about 25 : 26 m long.

EXERCISE 29C.1

1 Find the value ofx:

abc

2 In triangle ABC find:

a aifA=65o,B=35o,b=18cm b bifA=72o,C=27o,c=24cm

c cifB=25o,C=42o,a=7: 2 cm.

FINDING ANGLES

The problem of finding angles using the sine rule is more complicated because there may be two possible

answers.

Thisambiguous casemay occur when we are given two

sides and one angle, where the angle is opposite the shorter

side.

It occurs because an equation of the form sinμ= b

produces answers of the form μ= sin¡^1 b or

(180o¡sin¡^1 b).

A

B

C

41°

113°

18 m

15 cm

xcm

32°

46°

xcm

48°

108°

9cm

55° 6.3 km

84° xkm

-1 1

1

O

()-¡ab,

y

x

bb ()ab,¡

q q

586 Further trigonometry (Chapter 29)

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Y:\HAESE\IGCSE01\IG01_29\586IGCSE01_29.CDR Monday, 27 October 2008 2:52:46 PM PETER