Plane Geometry Problems With Solutions' title='Plane Geometry Problems With Solutions' />Sine Law to Solve Triangle Problems. Problem 1 A triangle ABC has angle A 1. Explore interactively topics in geometry. Geometry problems and tutorials with detailed solutions are also included. Graph Individual x,y Points powered by WebMath. B 3. 1 o and side a 1. Solve the triangle ABC by finding angle C and sides b and c. Solution to Problem 1 Use the fact that the sum of all three angles of a triangle is equal to 1. C. A B C 1. Solve for C. C 1. A B 4. 3 o. Use sine law to write an equation in b. A b sinB. Solve for b. B sinA approximately 5. Use the sine law to write an equation in c. A c sinC. Solve for c. C sinA approximately 7. Problem 2 The angle of elevation to the top C of a building from two points A and B on level ground are 5. The distance between points A and B is 3. Midi File Michael Buble more. Points A, B and C are in the same vertical plane. Find the height h of the buildinground your answer to the nearest unit. Solution to Problem 2 We consider triangle ABC. Angle B internal to triangle ABC is equal to. B 1. 80 o 6. 0 o 1. In the same triangle, angle C is given by. C 1. 80 o 5. Use sine law to find d. Solve for d. d 3. We now consider the right triangle. Solve for h. h d sin6. Substitute d by the expression found above. Use calculator to approximate h. Problem 3 A triangle ABC has side a 1. A 8. 0 o angle A is opposite side a. Find side c and angles B and C if possible. Solution to Problem 3 Use sine law to write an equation in sinB. A b sinB. Solve for sinB. B b a sinA 1. No real angle B satisfies the equationsin B 1. The given problem has no solution. Problem 4 A triangle ABC has side a 1. A 3. 2 o angle A is opposite side a. Find side c and angles B and C if possible. Solution to Problem 4 Use sine law to write an equation in sinB. A b sinB. Solve for sinB. B b a sinA 1. Two angles satisfy the equation sin B 0. B1 4. 6. 0 o and B2 1. Solution 1 Find angle C1 corresponding to B1. C1 1. 80 B1 A 1. Solution 1 Find side c. C1c. 1 sinC1 a sinA. Solution 2 Find angle C2 corresponding to B2. C2 1. 80 B2 A 1. Solution 2 Find side c. Antivirus Gratis Para Windows Xp 2000 Software. C2c. 2 sinC2 a sinA. Exercises 1. A triangle ABC has angle A 1. C 3. 3 o and side c 9 m. Solve the triangle ABC by finding angle B and sides a and b. Redo problem 2 with the distance between points A and B equal to 5. Solutions to above exercises. B 4. 3 o, a 1. More geometry references. Sine Law Calculator and Solver. Geometry Tutorials, Problems and Interactive Applets. Cosine Law Problems. Cosine Law Calculator and Solver.