5/24/2018

1

Objective:

•Solve oblique triangles by using the Law of Sines

•Use Area Formulas to find areas of triangles

So where did this come from? Let’s think…take a look at this triangle…what do we

already know?

Solve for y

xy

42˚ 36˚

10

Law of Sines

C

c

B

b

A

a

sinsinsin

A

a

bc

CB

Used with:SAA, ASA, and SSA Triangles

Solving a triangle with AAS Info.

210

a

C

AB

c

31°

20°

5/24/2018

2

Solving a triangle with ASA Info. A=48°, B= 22°, a=5

Solving a triangle with SSA Info.What is special about SSA triangles and congruency?

What different triangle cases can be made and how many solutions can they produce? These are called ambiguous cases (p. 627-628).

A< 90˚ A>90˚

Solving a triangle with SSA Info. a=6, b=7, and A=65°

Solving a triangle with SSA Info. a= 7.5, b=12, A= 35˚

5/24/2018

3

ApplicationAn airplane A takes off from carrier B and flies in a straight line for 12 km. At that instant, an observer on destroyer C, Located 5 km from the carrier, notes that the angle determined by the carrier, the destroyer (the vertex) and the plane is 37°. How far is the plane from the destroyer?

ApplicationA plane flying in a straight line parallel to the ground passes directly over point A and later directly over point B, which is 3 miles from A. A few minutes after the plane passes over B, the angle of elevation from A to the plane is 43° and the angle of elevation from B to the plane is 67°. How high is the plane at this moment?

The Area of a Triangle General:

With an angle C with adjacent sides of lengths a and b

Heron’s Formula:

Where s=½(a+b+c)

A 1

2absinC

A s(s a)(sb)(sc)

Find area with SAS info.

8 cm13 cm

130°

5/24/2018

4

Find area with SSS info.a=7, b=9, and c=12