MT_F4_9.1 Sine Rule_1a

Chapter 9 Solution of Triangles

9.1 Sine Rule abc
sin A sin B sin C

Or

sin A  sin B  sin C
abc

Example: abc
sin A sin B sin C
(a)
c 5
b sin 1100 sin 450

(b)

(c) 9 cm

sin   sin 450
96

(d)
sin   sin 
63

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Sine rule can be used to solve a triangle when

(i) two angles and one side are given (ii) two sides and one non-included angle

B are given B

aa

A CA C

b

1. Find the length of BC

BC  4.7
sin 640 sin 530

4.7
sin 530
 BC
 sin 640

BC  5.289 cm

2. Find ACB sin ACB  sin 710
3. Find the length of AC 3.4 7.6

sin ACB  sin 710 3.4

7.6
sin ACB  0.4230

ACB  25.020

BAC  1800  760  370
 670

AC  6.5
sin 760 sin 670

6.5
sin 670
 AC
 sin 760

AC  6.852 cm

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Homework: Work book page 140 – 141
1.(a) m  5.611 cm

(b) m  52.290
(c) m  9.331 cm
2. XY  55.344 cm