Solving Triangles

1
Solving Triangles

• Precalculus Practice Problems
• R. Sinn
• September 22, 2005

2
Problem Solving Overview

• Right Triangles
• Side-Side Known
• Trig Ratios for angles
• Pythagorean Theorem for 3rd side
• Angle-Side
• Trig Ratios for angle and sides
• Non-Right Triangles
• SAA, ASA
• Law of Sines
• SSA (ambiguous)
• Law of Sines
• SSS and SAS
• Law of Cosines

3
Solve the Triangle

• Hint Law of Sines

4
Solve the Triangle

• Hint Law of Sines

5
Solve the Triangle

• Problem Ambiguous!!
• SSA

6
Solution 1

• Angle C acute.

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Solution 2

• Angle C obtuse.

8
Solve the Triangle

• Hint Law of Cosines

9
Solve the Triangle

• Hint Law of Cosines

10
Solve the Triangle

• No hints!!

11
SSA Problems

• There are three possibilities
• No solutions
• One solution
• Two solutions
• See Page 507 for examples.
• Dont get fooled by SSA!!
• Use Law of Sines
• Double-Check at end