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

Mathematics

1 answer:

goldenfox [79]3 years ago

4 0

9514 1404 393

Answer:

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.

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.

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Therefore, the t-value is -3.2.

Now, we using a level of significance of 0.01, and a degree of freedom (df) of 34, we use the t-table to find the p-value for this results. (df = N -1; in this case, we take the smaller sample, which is 35, giving us 34 of df).

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