January 11, 2011

6.1 Continued…Law of Sines

Objective: 1) Use the law of sines to solve the ambiguous case of a triangle, 2) Find the area of a triangle.

Standard: Trigonometry 13.0, 14.0

January 11, 2011

The Ambiguous Case: SSA

SSA is not a congruency property from Geometry, so we need to be careful when solving a triangle given two sides and the NON-included angle.Three Possible Outcomes:· 1 Triangle formed· 2 Triangles formed· 0 Triangles formed

January 11, 2011

52°

1912

Here's how 2 triangles are formed.

0°232

January 11, 2011

The Test for SSA -How you determine the number of solutions:If opp ≥ adj, then __________

If opp < adj, then __________

The second solution:

A1 is the _______ angle found.

Second solution angle A2= _______

You will have to complete the problem twice!

Then find B1,

C1, and c1

Then find B2, C2, and c2

January 11, 2011

Ex. 1) Use the Law of Sines to find the missing sides and angles.A=110°, a=125, b=100

Solutions?

January 11, 2011

Ex. 2) Use the Law of Sines to find the missing sides and angles.A=76°, a=18, c=20

Solutions?

January 11, 2011

Ex. 3) Use the Law of Sines to find the missing sides and angles.A=48°, a=11.4, c=12.8

Solutions?

Continues…

January 11, 2011

Ex. 3B) Use the Law of Sines to find the missing sides and angles.A=48°, a=11.4, c=12.8

January 11, 2011

Summary for solutions to triangles…

0 solutions: you get an error!

1 solution: opp>adj and you get an answer.

2 solutions: opp<adj and you get an answer. Oh, and you need to do the problem twice!

January 11, 2011

One more thing…The area of a triangle:

With our new-found Law of Sines, we can also use:

January 11, 2011

Ex. 4) Find the area of the triangle if A=74°, b=103 ft. and c=58 ft.

January 11, 2011

Homework:

#2 Law of Sines WS #11-30 (start at #21)