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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:  AC = AB + BC - 2 x AB x BC cos B

 

Hence   AC = 5 + 7 - 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:

    1. Try and use values given as much as possible to ensure greater accuracy in answers
    2. Do the calculation all in one step on the calculator to avoid rounding errors.
    3. 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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