Question

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

Answer 1

9514 1404 393

Answer:

• A = 27.1°
• B = 58.8°
• C = 94.1°

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°).