Download MATHEMATICS SUPPORT CENTRE Title: Sine Rule

T6
MATHEMATICS
SUPPORT CENTRE
Title: Sine Rule
Target: On completion of this worksheet you should be able to use the sine rule to
find the sides and angles of a triangle.
Given
Remember: In any triangle the longest
side is opposite the largest angle and the
shortest side is opposite the smallest
angle.
A
c
b
B
C
a
The sine rule states:
a
b
c
=
=
sin A sin B sin C
or
sin A sin B sin C
=
=
a
b
c
Exercise
Using the triangle opposite:
1. A = 750, C = 500 and c = 12cm.
Find a.
2. B = 300, C = 400 and a = 5·3m.
Find all the angles and sides.
(Answers: 1. 15·1cm, A=1100 b=2·82m
c=3·63m)
Examples
Example
Using the above triangle:
If A = 400, B = 800 and b = 15cm find c.
b
c
=
as we know
sin B sin C
length b, angle B and want to find c.
Angle C = (180 – 40 – 80)0 = 600
So
15
c
=
0
sin 80
sin 60 0
15
c=
× sin 60 0
0
sin 80
= 13 ⋅1907....
= 13 ⋅ 2cm
We will use
2. Solve triangle ABC if B = 350,
b = 95mm and c = 112mm.
Mathematics Support Centre,Coventry University, 2001
Solving a triangle means finding all the
1. Find B if C = 850, b=17cm and c=21cm.
We know that B < 850 because b < c
Using the sine rule
sin B sin C
=
b
c
sin B sin 85 0
=
17
21
sin 85 0
sin B =
× 17
21
B = 53 ⋅ 749...
B = 54 0 to the nearest degree
continued overleaf
Exercises
Solve the following triangles. All questions
refer to the triangle overleaf. (Hint: draw a
separate diagram for each question )
Mathematics Support Centre,Coventry University, 2001