Answer:
- A = 80.9°
- C = 43.1°
- a = 20.2
Explanation:
You want the missing side and angle measures in triangle ABC with AB = 14, AC = 17, and B = 56°.
Law of Sines
The law of sines tells you side lengths are proportional to the sine of their opposite angle:
a/sin(A) = b/sin(B) = c/sin(C)
Angle C
Side c is given, so we can find missing angle C from ...
C = arcsin(c/b·sin(B)) = arcsin(17/14·sin(56°)) ≈ 43.1°
Angle A
Angle A brings the sum of angles to 180°:
A = 180° -56° -43.1° = 80.9°
Side a
Now we have the information required to find side 'a':
a = b·sin(A)/sin(B) = 17·sin(80.9°)/sin(56°) ≈ 20.2
The missing measures are (A, C, a) = (80.9°, 43.1°, 20.2).
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Additional comment
We have only rounded the final values in the computations. Intermediate values are used to full calculator precision.