Students Take out your calendar and your homework

Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary. 1) Find the measure of each angle. Find the missing parts of each triangle. 2)

Digital Lesson Law of Sines

An oblique triangle is a triangle that has no right angles. C a b A c B To solve an oblique triangle, you need to know the measure of at least one side and the measures of any other two parts of the triangle – two sides, two angles, or one angle and one side.

The following cases are considered when solving oblique triangles. 1. Two angles and any side (AAS or ASA) A A c c B C 2. Two sides and an angle opposite one of them (SSA) c C 3. Three sides (SSS) b a c a 4. Two sides and their included angle (SAS) c a B

The first two cases can be solved using the Law of Sines. (The last two cases can be solved using the Law of Cosines. ) Law of Sines If ABC is an oblique triangle with sides a, b, and c, then C b A h C a c Acute Triangle h B b a c A Obtuse Triangle B

Example (ASA): Find the remaining angle and sides of the triangle. The third angle in the triangle is A = 180 – A – B = 180 – 10 – 60 = 110. C 10 a = 4. 5 ft 4. 15 ft b 110 A Use the Law of Sines to find side b and c. 60 c 0. 83 ft B

Example (SSA): Use the Law of Sines to solve the triangle. A = 110 , a = 125 inches, b = 100 inches C 21. 26 a = 125 in b = 100 in 110 A C 180 – 110 – 48. 74 = 21. 26 48. 74 c 48. 23 in B

Example (SSA): Use the Law of Sines to solve the triangle. A = 76 , a = 18 inches, b = 20 inches C b = 20 in a = 18 in 76 B There is no angle whose sine is 1. 078. There is no triangle satisfying the given conditions. A

Area of an Oblique Triangle C Example: Find the area of the triangle. A = 74 , b = 103 inches, c = 58 inches 103 in a b A 74 c 58 in B

Application: A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 14 with the horizontal. The flagpole casts a 16 -meter shadow up the slope when the angle of elevation from the tip of the shadow to the sun is 20. A 20 70 Flagpole height: b 14 C 34 B 16 m The flagpole is approximately 9. 5 meters tall.

Complete each identity.

Example (SSA): Use the Law of Sines to solve the triangle. A = 58 , a = 11. 4 cm, b = 12. 8 cm C 49. 8 b = 12. 8 cm a = 11. 4 cm B 1 72. 2 58 c A 10. 3 cm C 180 – 58 – 72. 2 = 49. 8 Two different triangles can be formed. Example continues.

Example (SSA) continued: Use the Law of Sines to solve the second triangle. A = 58 , a = 11. 4 cm, b = 12. 8 cm B 2 180 – 72. 2 = 107. 8 C 49. 8 b = 12. 8 cm a = 11. 4 cm C 180 – 58 – 107. 8 = 14. 2 72. 2 58 c A B 1 10. 3 cm C 14. 2 b = 12. 8 cm a = 11. 4 cm 58 107. 8 B 2 c 3. 3 cm A