TRIGONOMETRY: SINE RULE
The purpose of this worksheet is to discover a formula called Sine Rule.
Section A: Exploration
1.
Draw any triangle in the space below. It does not matter whether it is right-angled, acuteangled, obtuse-angled, equilateral, isosceles or scalene. But try to draw as big as possible.
2.
Label the vertices of the triangle A, B and C (the order does not matter).
3.
Label the side of the triangle opposite the vertex A as a (the order is important).
Label the side of the triangle opposite the vertex B as b.
Label the side of the triangle opposite the vertex C as c.
4.
Using a protractor and a ruler, complete the table below. Your measurements will be
different from your teacher or your classmates.
Angle
5.
Angle in Degrees
Length of Side
A
a
B
b
C
c
Length in cm
Using a calculator, evaluate the expressions in the table below.
Expression
a
sin A
b
sin B
c
sin C
Value (to 2 s.f.)
© Joseph Yeo, 1998-2010: This worksheet is FREE for anyone to use
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Section B: Findings
6.
What do you notice about the values of the 3 expressions in the table in Q5?
7.
Check the value of
8.
Check the values of all the 3 expressions with your classmate. What do you notice?
9.
Does your finding in Q6 and Q8 depend on which triangle you or your classmate draw?
10.
The relationship that you have discovered in Q6 and Q8 is called the Sine Rule. State the Sine
Rule in the box below.
a
with a classmate. Does it have the same value? ____________
sin A
Section C: Application
11.
Do you think the relationship
sin A sin B sin C
is also true? Why or why not?


a
b
c
© Joseph Yeo, 1998-2010: This worksheet is FREE for anyone to use
Page 2
Answer Keys
6.
7.
8.
9.
Equal
No
Equal
No
10.
a
b
c


sin A sin B sin C
11.
Yes
© Joseph Yeo, 1998-2010: This worksheet is FREE for anyone to use
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