Law of Sines

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Law of Sines

• Section 6.1

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Learning Goal

• I will be able to solve a triangle.

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Why?

• Solving triangles is an important part of
  surveying and navigation.

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Oblique Triangles
We know how to solve a right triangle. But, what
if the triangle isnt right? We need a method
that will work for what we call oblique
triangles.
(Triangles that arent right)
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Given ?ABC with obtuse angle b
Draw altitude BD let it be known as h1 Angles
ADB and CDB are right angles by definition of
altitude.
We can extend this to all angles in any triangle
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The Law of Sines
OR
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Example 1
given AAS
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Example 2
OR
given SSA
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Ambiguous Case
When two sides and a non-included angle (SSA) are
given, there are several situations possible
this is the ambiguous case.
There could be only one triangle. There could be
two triangles (when you can fit the alternate
angle in a triangle). There could be no triangle
(when you take the inverse sine of a value larger
than 1).
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Section 6.1, The Ambiguous Case (SSA) Table, pg.
394
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Navigational Bearing
There are two methods of expressing bearing in
proper navigational style.
One, as an acute angle from a cardinal
direction. Example S 35 E (aka 35 E of S)
Two, as an angle measured clockwise from north.
(Known as air navigation.) Example 315
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Example 3
A forest ranger at an observation point (A)
sights a fire in the direction 32 east of north.
Another ranger at a second observation point
(B), 10 miles due east of A, sights the same fire
48 west of north. Find the distance from each
observation point to the fire.
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Learning Goal

• I will be able to solve a triangle.

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End of Notes.

• Homework p.398 Vocabulary Check 1, 2, and
  Exercises 1, 3, 7, 9, 15, 17, 19, 27, 29, 31