Solve the triangle. a = 10, b = 23, C = 95° (2 points) c ≈ 25.1, A ≈ 26.8°, B ≈ 58.2° c ≈ 25.1, A ≈ 22.8°, B ≈ 62.2° c ≈ 25.9, A
≈ 22.8°, B ≈ 62.2° c ≈ 25.9, A ≈ 59.2°, B ≈ 25.8°
1 answer:
Answer:
c ≈ 25.9, A ≈ 22.8°, B ≈ 62.2°
Step-by-step explanation:
The Law of Cosines can be used to find the third side.
... c² = a² + b² - 2ab·cos(C)
... c² ≈ 100 +529 -2·10·23·cos(95°)
... c² ≈ 669.0916
... c ≈ √669.0916 ≈ 25.87
From the Law of Sines, we can find the remaining angles.
... sin(B)/b = sin(C)/c
... B = arcsin(b/c·sin(C)) ≈ 62.35°
These results are sufficient to make the appropriate answer choice.
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<em>Comment on Answer Discrepancies</em>
If the "c" used in the calculation of B is inappropriately rounded to 25.9, then the result for angle B is 62.21°. This is in error by more than 0.1°. Intermediate results should <em>never</em> be rounded, but should be carried to full calculator precision. Only final answers should be rounded.
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