Cambridge International Mathematics

4 Find:

a the smallest angle of a triangle with sides 9 cm, 11 cm and 13 cm

b the largest angle of a triangle with sides 3 cm, 5 cm and 7 cm.

5aUse the cosine rule in triangle BCM to findcosμin terms

ofa,candm.

b Use the cosine rule in triangle ACM to find cos(180o¡μ)

in terms ofb,candm:

c Use the fact that cos(180o¡μ)=¡cosμ to prove

Apollonius’ median theorem:

a^2 +b^2 =2m^2 +2c^2.

d Hence findxin the following:

iii

6 In triangle ABC, AB=10cm, AC=9cm and AbBC=60o. Let BC=xcm.

a Use the cosine rule to show thatxis a solution of x^2 ¡ 10 x+19=0.

b Solve the above equation forx.

c Use a scale diagram and a compass to explain why there are two possible values ofx.

7 Find, correct to 3 significant figures, the area of:

ab

Whenever there is a choice between using the sine rule or the cosine rule, always use thecosine ruleto

avoid the ambiguous case.

Example 10 Self Tutor

An aircraft flies 74 km on a bearing 038 oand then 63 km on a bearing 160 o.

Find the distance of the aircraft from its starting point.

PROBLEM SOLVING WITH THE

SINE AND COSINE RULES

E

CB

A

b

m

a

c

c

q

M

180 ¡-¡q°

12 cm

xcm 9cm

5cm

8m

8m

10 m

xm

2cm

3cm

4cm

4cm

5cm

6cm

Further trigonometry (Chapter 29) 591

[8.4, 8.5, 8.7]

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Y:\HAESE\IGCSE01\IG01_29\591IGCSE01_29.CDR Tuesday, 18 November 2008 11:08:11 AM PETER