mikesleviticus08
27.06.2021 •
Mathematics
consider a triangle ABC. Suppose that a=16, b=30, and c=35. Solve the triangle. Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth
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Ответ:
9514 1404 393
A = 27.1°B = 58.8°C = 94.1°Step-by-step explanation:
An angle can be found using the Law of Cosines.
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab)) = arccos((16² +30² -35²)/(2·16·30))
C = arccos(-69/960) ≈ 94.1217°
Then another angle can be found using the Law of Sines:
sin(B)/b = sin(C)/c
B = arcsin(b/c·sin(C)) ≈ 57.7516°
The third angle can be found from the sum of angles of a triangle.
A = 180° -94.1217° -58.7516° = 27.1267°
The angles of the triangle are about (A, B, C) = (27.1°, 57.8°, 94.1°).
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