
IB
MATH STUDIES
GEOMETRY AND TRIGONOMETRY
WORKED EXAMPLES FOR THE SINE
AND COSINE RULE
Given
the triangle ABC as shown
Given triangle ABC
where AB = 5cm and BC = 7cm and angle C = 40° Find 
a. 
Angle A 
b. 
AC 
c. 
Area of triangle ABC 
First sketch the triangle with the information given
(Diagram
not to scale) 

a. 
Using the sine rule:



b. 
To
find AC we can use the sine or cosine rule as we now no that angle
B = 180  40 64.1 =75.9° 

Using the cosine
rule: AC² = AB² + BC²  2 x AB x BC cos B 

Hence AC² = 5² + 7²  2x5x7 cos 75.9 

AC
= 7.55 cm
(correct to 3 significant figures) 

Using Sine rule
(there is a slight difference in values) 
c. 
Area triangle ABC




Notes:

Try and
use values given as much as possible to ensure greater
accuracy in answers

Do the
calculation all in one step on the calculator to avoid
rounding errors.

Remember
brackets on the calculator. Example sin40 should be
entered as sin(40)



Useful rules:
1. The largest
angle is opposite the largest side, also the smallest angle
is opposite the shortest side
2. The two right
angled triangles with sides in the ratio 3:4:5 and 5:12:13 

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