Math 20: Foundations FM20.5 Demonstrate understanding of the cosine law and sine law (including the...
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Math 20: Foundations FM20.5 Demonstrate understanding of the cosine law and sine law (including the ambiguous case). D. The Trigonometric Legal Department
Math 20: Foundations FM20.5 Demonstrate understanding of the
cosine law and sine law (including the ambiguous case). D. The
Trigonometric Legal Department
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Starting Point Lacrosse Trigonometry p.114
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1. How are Sides and Angles of a Triangle Related? FM20.5
Demonstrate understanding of the cosine law and sine law.
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What are two equivalent expressions that represent the height
of ABC ?
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Summary p.117
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Practice Ex. 3.1 (p.117) # 1-5
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2. The Law of Sines FM20.5 Demonstrate understanding of the
cosine law and sine law (including the ambiguous case).
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2. The Law of Sines Last day we discovered a side-angle
relationship in acute triangles. Before we can use this to solve
problems we have to prove it is true for all acute triangles
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Example 1
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Example 2
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**Note:
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Example 3
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Summary p.124
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Practice Ex. 3.2 (p.124) #1-15 #4-19
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3. The Cosine Law! FM20.5 Demonstrate understanding of the
cosine law and sine law (including the ambiguous case).
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3. The Cosine Law! Unfortunately the Sine Law will not work for
all situations.
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For example.
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For these situations another Relationship was created called
the Cosine Law Again we must prove it before we can use it.
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The Cosine Law is: Used when you have: 2 sides and included
angle All 3 sides.
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Explain why you can use the cosine law to solve for side q in
QRS and for F in DEF on page 130.
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Example 1
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Example 2
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Example 3
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Summary p.137
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Practice Ex. 3.3 (p.136) #1-14 #4-17
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4. Use Triangles to Solve the Problem FM20.5 Demonstrate
understanding of the cosine law and sine law (including the
ambiguous case).
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4. Use Triangles to Solve the Problem
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Example 1
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Example 2
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Summary p.146
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Practice Ex. 3.4 (p.147) #1-14 #3-17
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5. What about Obtuse Triangles FM20.5 Demonstrate understanding
of the cosine law and sine law (including the ambiguous case).
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* Until now, you have used the primary trigonometric ratios
only with acute angles. For example, you have used these ratios to
determine the side lengths and angle measures in right triangles,
and you have used the sine and cosine laws to determine the side
lengths and angle measures in acute oblique triangles.
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Lets investigate the values of the primary trig ratios for
obtuse triangles Evaluate sin100 However there is not right
triangle that can be made with a 100 angle
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However we can make a right triangle with its supplement 80
What is sin80?
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Complete the chart on p. 163 and the reflection questions that
follow.
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Summary p.163
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Practice Ex. 4.1 (p.163) #1-4
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6. Do the Sin and Cos Laws Work for Obtuse Triangles? FM20.5
Demonstrate understanding of the cosine law and sine law (including
the ambiguous case).
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6. Do the Sin and Cos Laws Work for Obtuse Triangles? In
section 3 we proved the Sin Ratio for Acute triangles. We are going
to adjust that proof to prove the Sin Law for Obtuse
Triangles.
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Example 1
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Example 2 Determine the distance between Jaun and the
Balloon.
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Lets now look to see if the Cosine Law holds true for Obtuse
Triangles
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Example 3
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Summary p.170
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Practice Ex. 4.2 (p.170) #1-5 evens in each, 6-15 #3-17
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7. How Many Triangles Exist? (The Ambiguous Case) FM20.5
Demonstrate understanding of the cosine law and sine law (including
the ambiguous case).
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7. How Many Triangles Exist? (The Ambiguous Case) Ambiguous
Case A situation in which two triangles can be drawn, given the
available information; the ambiguous case may occur when the given
measurements are the lengths of two sides and the measure of an
angle that is not contained by the two sides (ASS).
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So when you are dealing with the Ambiguous Case and given SSA
as your information there are 4 possible solutions 1 Oblique
Triangle 1 Right Triangle 2 Triangles No Triangles
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How do we figure out how many triangles are possible given the
Ambiguous Case (SSA)?
