How to Easily Setup and Solve 2 Triangles in the SSA Ambiguous Case

Unravel the mysteries of the Side-Side-Angle (SSA) ambiguous case in trigonometry when two triangles are possible! Mario's Math Tutoring guides you through drawing and solving both possible triangles using the Law of Sines. Learn how to determine if two triangles exist by comparing the given side length to the altitude, and then meticulously solve for all missing angles and side lengths in both scenarios. In this video, you'll discover: 0:00 Introduction to the SSA Ambiguous Case (Two Triangles) 0:30 Setting Up the Initial Triangle Diagram 1:00 How to Determine if Two Triangles Exist (Comparing Side 'a' to the Altitude 'h') 1:30 Calculating the Altitude (h) using Sine 2:00 Conditions for Two Triangles 2:30 Visualizing the Two Possible Triangles 3:00 Drawing Both Triangles for Clarity 3:50 Step 1: Solving for Angle B using the Law of Sines 4:50 Important: Finding the Second Possible Angle B (180° - B) 5:20 Using Isosceles Triangle Properties to Understand the Second Angle 5:40 Step 2: Solving for Angle C in Both Triangles (180° - A - B) 6:30 Step 3: Solving for Side C in Both Triangles using the Law of Sines 7:00 Example 1: Solving for Two Triangles (Angle A = 32°, a = 7, b = 11) 8:00 Example 2: Solving for Two Triangles (Angle C = 47°, c = 9, b = 12) 8:30 Verifying Two Triangles by Calculating the Altitude 9:20 Solving for Angle B in Example 2 10:00 Solving for Angle A and Side A in Both Triangles of Example 2 Master the SSA ambiguous case and confidently solve for all missing parts of two possible triangles! #SSAAambiguousCase #LawOfSines #Trigonometry #SolvingTriangles #Precalculus #MathTutorial #MathHelp ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join