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IB
MATH STUDIES
GEOMETRY AND TRIGONOMETRY
WORKED EXAMPLES FOR THE SINE
AND COSINE RULE
Given
the triangle ABC as shown
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Given triangle ABC
where AB = 5cm and BC = 7cm and angle C = 40° Find |
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a. |
Angle A |
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b. |
AC |
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c. |
Area of triangle ABC |
First sketch the triangle with the information given
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not to scale) |
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| a. |
Using the sine rule:
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| 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° |
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Using the cosine
rule: AC² = AB² + BC² - 2 x AB x BC cos B |
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Hence AC² = 5² + 7² - 2x5x7 cos 75.9 |
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AC
= 7.55 cm
(correct to 3 significant figures) |
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Using Sine rule
(there is a slight difference in values) |
| c. |
Area triangle ABC
 |
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Notes:
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Try and
use values given as much as possible to ensure greater
accuracy in answers
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Do the
calculation all in one step on the calculator to avoid
rounding errors.
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Remember
brackets on the calculator. Example sin40 should be
entered as sin(40)
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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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