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Notes Over 8.1. Solving Oblique Triangles. To solve an oblique triangle , you need to be given one side, and at least two other parts (sides or angles). 4 cases for oblique triangles. 1. Two angles and any side (AAS or ASA). C. 2. Two sides and an angle opposite one of them (SSA). a. b.

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Notes Over 8.1

Solving Oblique Triangles

To solve an oblique triangle , you need to be given one side, and at least two other parts (sides or angles).

4 cases for oblique triangles

1. Two angles and any side (AAS or ASA)

C

2. Two sides and an angle opposite one of them (SSA)

a

b

3. Three sides (SSS)

A

B

4. Two sides and their included angle (SAS)

c

The first two cases use Law of Sines, the last two will use the Law of Cosines.


Notes Over 8.1

Law of Sines

If ABC is a triangle with sides a, b, c, then according to the law of sines,

or


Notes Over 8.1

The AAS or ASA Case

Solve ∆ABC

Find:


Notes Over 8.1

The AAS or ASA Case

Solve ∆ABC

Find:


Notes Over 8.1

The Ambiguous Case (SSA)

Consider a triangle where you are given a, b, and A

A is acute

If the height of the triangle h were equal to a, then it would be a right triangle.

a

b

a

a

a

h

a

A

If a < h, then there would be no triangle.

If a > b, then there would be one triangle.

If h < a < b, then there would be two triangles.


Notes Over 8.1

The SSA Case – One Triangle

Solve ∆ABC

Since a > c, one triangle.

Find:


Notes Over 8.1

The SSA Case – Two Triangles

Solve ∆ABC

Find h.

Since a < h, no triangle.


Notes Over 8.1

The SSA Case – Two Triangles

Solve ∆ABC

Find h.

Since h < a < b, two triangles


Notes Over 8.1

Area of an Oblique Triangle

For any triangle, given two sides and the included angle

  • Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102o.


Notes Over 8.1

Pg. 588, 8.1 #1-18 all


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