The Ambiguous SSA Triangle - Given an Obtuse Angle
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The Ambiguous SSA Triangle – Given an Obtuse Angle
When given a SSA triangle with sides \(a\), \(b\) and \(\angle A\), which is obtuse, two cases are possible.
Case 1: \(a \le b\)
If the side opposite the given angle is less than or equal to the other given side \((a \le b)\), then there is no solution since no triangle is possible.
Case 2: \(a > b\)
If the side opposite the given angle is greater than the other given side \((a > b)\), then exactly one triangle is defined, so there is one solution.
Key Lesson Marker |
Given a SSA triangle such as \(\triangle ABC\), and angle \(A\) is obtuse:
| Situation | Number of solutions
|
| \(a \le b\) |
No solution
|
| \(a > b\) |
One solution
|