Solve triangle problems using the sine law . A tutorial with problems, detailed solutions and exercises with answers. The ambiguous case of the sine law, where two sides and one angle are given, is also considered (problems 3 and 4).

Problem 1A triangle ABC has angle A = 106 ^{ o}, angle B = 31 ^{ o} and side a = 10 cm. Solve the triangle ABC by finding angle C and sides b and c.(round answers to 1 decimal place).Solution to Problem 1:
Problem 2The angle of elevation to the top C of a building from two points A and B on level ground are 50 degrees and 60 degrees respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building(round your answer to the nearest unit).Solution to Problem 2:
Problem 3A triangle ABC has side a = 12 cm, side b = 19 cm and angle A = 80 ^{ o} (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).Solution to Problem 3:
Problem 4A triangle ABC has side a = 14 cm, side b = 19 cm and angle A = 32 ^{ o} (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).Solution to Problem 4
Exercises1. A triangle ABC has angle A = 104 ^{ o}, angle C = 33 ^{ o} and side c = 9 m. Solve the triangle ABC by finding angle B and sides a and b.(round answers to 1 decimal place).2. Redo problem 2 with the distance between points A and B equal to 50 meters.
Solutions to Above Exercises1. B = 43 ^{ o}, a = 16.0 m , b = 11.3 m2. 191 meters.
More References and Links to Sine and Cosine Lawssine lawSine Law Calculator and Solver. Geometry Tutorials, Problems and Interactive Applets. Cosine Law Problems. Cosine Law Calculator and Solver. 