Law of Sines Homework

Law of Sines & Cosines Homework Worksheet Law of Sines: ______Law of Cosines:______, ______, ______Questions: Answer the questions and justify your answers. 1. To use the Law of Sines, you 2. Is it possible to solve a triangle 3. Why is it not generally must know the measures of at if you only know the measures of possible to use the Law of Sines least… the three angles in the triangle? to solve a triangle for which one only knows the measures of all of the sides in a triangle?

4. When should you use the Law 5. To solve a triangle in which two sides and the included angle are of Cosines to solve a triangle? given, your tutor suggests that you… 1. Use Law of Cosines to find the largest angle. 2. Use Law of Sines to find another angle. 3. Find the third angle by using the formula 180° – A° – B° = C°. Why is this easier than using the Law of Cosines to find all of the angles of the triangle?

6. Compare and contrast when the given information to solve a triangle indicates using the Law of Sines versus using the Law of Cosines.

Solve the triangles. 7. β = = 82°, b = 6, c = 3 8. α = 42°, a = 10, c = 18 9. γ = 32°, a = 14, c = 9

10. a = 4, b = 3, c = 6

11. To find the distance across a canyon, a 12. A surveyor walks 380 meters from point A to surveying team locates points A and B on one side point B. Then the surveyor turns 80° to the left of the canyon and point C on the other side of the and walks 240 meters to point C, as in the figure canyon. The distance between points A and B is 85 below. What is the approximate length of the yards. The measure of  CAB = 68°, and the marsh? measure of  ABC = 75°. What is the distance across the canyon?