Sine Law - Ambiguous Case (SSA)

We have seen that using the Law of Sines with the combinations [u][b][color=#6aa84f]ASA and AAS[/color][/b][/u]guarantees one unique solution and one unique triangle. Working with the third option of SSA, however, leaves the door open for several different situations and solutions to occur. [br][br]For this reason, [color=#ff0000]SSA [/color]is referred to as the [color=#0000ff][b][u]Ambiguous Case.[/u][/b][/color][br]
Investigate the Ambiguity! [Part 1]
Using your knowledge of the law of sine, solve for the missing parts of the triangle. Show your triangle in your paper. [br][br][i]Remember that this is collaborative learning. Share all information with your groupmates. [br][br][/i][b][color=#0000ff]Given: a = 5, b = 7, & ∠A = 140°[br][/color][/b][br][b]Question: Compute for ∠B. [br][/b]Follow the solutions below:[br][img]data:image/png;base64,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[/img]
Now, add the measurements of [b]∠A and [/b][b]∠B. [br][/b]What's your answer? [br]Does this make sense? Why or Why not?
What does this imply? [b]Will you be able to form a triangle if this is the case?[/b] If so, how many? [br][i]Summarize your answer as a group. [/i]
Investigate the Ambiguity! [Part 2]
Using your knowledge of the law of sine, solve for the missing parts of the triangle. Show your triangle in your paper. [br][br][i]Remember that this is collaborative learning. Share all information with your groupmates. [br][br][/i][b][color=#0000ff]Given: a = 15, b = 12, & ∠A = 68°[br][/color][/b][br][b]Question: Compute for ∠B. [br][/b][i]Follow the solutions below:[br][img]data:image/png;base64,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[/img][br][br][br][/i]
Now, add the measurements of [b]∠A and [/b][b]∠B. [br][/b]What's your answer? [br]Does this make sense? Why or Why not?
A triangle will be formed using the given information earlier ([b][color=#0000ff]a = 15, b = 12, & ∠A = 68°[/color][/b]). This is how it looks like:[br][img]data:image/png;base64,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[/img] with [b][color=#0000ff]∠A = 68°, [/color][b][color=#ff0000]∠B = 47.88°[/color][color=#0000ff], [/color][b][color=#ff7700]∠C = 180 - 68 - 47.88 = 64.12[/color][/b][/b][/b][br][br][b]PONDER ON THIS! Is it possible that another triangle can be formed using the same given? [br]Let's find out! [/b]
To know if there will be another triangle that can be formed using the same given, get the supplement of [b]∠B. [/b][u][color=#0000ff]That is, subtract your answer for ∠B to 180°. [/color][/u]What's your answer? [br][br]
Now, add the [color=#0000ff][b]supplement of [/b][/color][b]∠B [/b]to the measure of [b]∠A. What did you get? [br][/b][i]Hint: 68° + [color=#0000ff][b]supplement of [/b][/color][b]∠B [/b] =[color=#ff7700]Answer[/color][/i]
If the [b][color=#ff7700]supplement of the computed angle[/color][/b] is added to the [b]original given angle [/b]and it sums up [b][color=#0000ff]less than 180 degrees, [/color]then you have a second triangle. [br][br][/b]If this is not the case ([color=#0000ff][b]sum is greater than 180 degrees[/b][/color]), then only one triangle can be formed. [br][br][b]QUESTION: Going back to your previous answer, will there be a second triangle that can be formed using the same given information?[/b]
In your own words, summarize your learnings for today by answering the questions below:[br]1. When will we know when [b]no triangle[/b] will exist using the given information?[br]2. When will we know when [b]exactly ONE triangle[/b] will exist using the given information?[br]3. When will we know when there could be [b]TWO different triangles [/b]that will exist using the given information?[br]
WATCH ME! [OPTIONAL]
Law of Sine - Ambiguous Case [OPTIONAL]
Steps on how to solve the ambiguity of SSA case:[br]1. Find the second angle of the triangle. If it doesn't make sense, then there's no triangle.[br]2. See if the supplementary angle of that angle can also make a triangle. If so, then there are two triangles. If not, then there's just one triangle.[br]3. Solve for the rest of the triangle(s) using the Law of Sines.
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Information: Sine Law - Ambiguous Case (SSA)