Download The Cosine Rule

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The Cosine Rule
Monday 6th October 2014
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Labeling you triangle
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It is important that you label correctly. Angles are
represented by capital letters and lengths are represented
by lower case letters.
B
Each angle will correspond
to the length opposite.
c
A
a
b
C
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Trigonometry in Real Life
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https://www.youtube.com/watch?v=WehHFJki9yQ
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The cosine Rule
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a2=b2+c2-2bc cos A
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We use this formula to calculate a missing length in a triangle.
C
b
13 cm
Firstly label your triangle.
a
x
76°
A
7 cm
c
B
Then you need to substitute the values
into the formula:
a2= 132+72 – 2×13×7×cos76
Now you need your calculator.
Make sure it is in degree mode!
a2= 67.9716977384
a= 8.24449499596
a=8.24cm
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Your turn
Amber:
Green:
Find the length of the missing
side:
A man starts at the village of
Lymm and walks 5 km due South
to Dunham. Then he walks
another 8 km on a bearing of
130° to Mire.
What is the direct distance
between Lymm and Mire, in a
straight line?
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Finding a missing angle
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First we need to be able to rearrange the formula.
a2=b2+c2-2bc cos A
Rearrange to make cos A the subject of the formula
a2=b2+c2-2bc cos A (+2bc cosA)
a2+2bc cosA=b2+c2 (-a2)
2bc cosA=b2+c2-a2 (÷2bc)
cosA=(b2+c2-a2)÷(2bc)
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Calculating a missing angle
cos A=(62+102-92)÷(2×6×10)
cos A= 0.45833333333333
A=62.720387264
A=62.7°
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Your turn
Amber:
Green:
Find the missing angles.
A triangle has two sides of
length 30cm and an angle of
50°. Unfortunately the
position of the angle is not
known. Sketch two possible
triangles and use them to
work out the two possible
lengths of the third side of the
triangle.
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Exam Question
A, B, C and D are four points on a circle.
ABX and DCX are straight lines.
AB = 7 cm, BX = 5 cm and CX = 6 cm.
Angle BXC = 28°
(a) Calculate the length of AC.
Give your answer correct to 3 significant
figures.
(3)
(b) Calculate the length of DC.
(3)
(Total for question = 6 marks)