Determine the number of triangles ABC possible with the given parts.
b = 24, c = 29, B = 43°

9514 1404 393

  2

Step-by-step explanation:

In general, if the given angle is opposite the shorter 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 longer of the two given sides, there is one possible triangle. The same is true if the given angle is between the two given sides.

so, converting firstly the mixed fractions to improper fractions and then "adding".