Determine the number of triangles ABC possible with the given parts. b = 24, c = 29, B = 43°
1 answer:
9514 1404 393
Answer:
2
Step-by-step explanation:
In general, if the given angle is opposite the <em>shorter</em> of the two given sides, there will be 0 or 2 possible triangles. The attachments show the two possibilities.
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There will be zero possible triangles if the ratio of sides is less than the sine of the angle. Here, 24/29 ≈ 0.8276, sin(43°) ≈ 0.6820. The ratio of sides is greater, so there are two possible triangles.
If the given angle is opposite the <em>longer</em> of the two given sides, there is one possible triangle. The same is true if the given angle is <em>between</em> the two given sides.
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