Question

When using the law of sines, why can the SSA case result in zero, one, or two triangles? Explain.

Answer 1

Answer:  If you have SSA, then the third side determines the triangle. If it is too short to intersect the other side, then it does not form a triangle. The third side can also be just the right length to meet the other side, making one triangle. Finally, the third side might be long enough to intersect the other side at two different points, creating two triangles.

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Answer 2

Answer:

Let we have two sides 'a' and 'b' and an angle α, β opposite 'a' and 'b'.

Then the law of sines states that:

$\frac{a}{sin\alpha }$=$\frac{b}{sin\beta }$

For triangle angles, the sine is always positive.

The expression may give value exactly equal to 1 which means α=90°, therefore the question determines exactly one triangle that is the the right triangle.

For sinα<1, there are two triangle angles with the  principal angle in the first quadrant and the other in the second quadrant.

sinβ=0 is the special case and called degenerate triangle.

Step-by-step explanation: