Cambridge International Mathematics

For the obtuse angled triangle ABC alongside:

Area of triangle ABC=^12 £AB£CN=^12 ch

But sin(180o¡A)=

h

b

) h=bsin(180o¡A)=bsinA

) area of triangle ABC=^12 cbsinA,

which is the same result as whenAwas acute.

Summary:

The area of a triangle is a half of the product of

two sides and the sine of the included angle.

Example 4 Self Tutor

Find the area of triangle ABC.

Area=^12 acsinB

=^12 £ 15 £ 11 £sin 28o

¼ 38 : 7 cm^2

EXERCISE 29B

1 Find the area of:

abc

de f

A

A

()180 ¡-¡° A

NB

C

h

b

a

c

side included angle

side

A

B C

11 cm

15 cm

28°

12 cm

13 cm

45°

28 km

82°

25 km

7.8 cm

112°

6.4 cm

1.65 m

78°

1.43 m

12.2 cm

10.6 cm 125°

32 m 84° 27 m

584 Further trigonometry (Chapter 29)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_29\584IGCSE01_29.CDR Monday, 27 October 2008 2:52:41 PM PETER