1. Holt Geometry 8-5 Law of Sines and Law of Cosines Warm Up 1. What is the third angle measure in a triangle with angles measuring 65° and 43°? Find each value. Round trigonometric ratios to the nearest hundredth and angle measures to the nearest degree. 2. sin 73°3. cos 18°4. tan 82° 5. sin -1 (0.34)6. cos -1 (0.63)7. tan -1 (2.75)

2. Holt Geometry 8-5 Law of Sines and Law of Cosines Use the Law of Sines and the Law of Cosines to solve triangles. Objective

3. Holt Geometry 8-5 Law of Sines and Law of Cosines Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. A. tan 103° B. cos 165° C. sin 93° tan 103°  –4.33cos 165°  –0.97sin 93°  1.00

4. Holt Geometry 8-5 Law of Sines and Law of Cosines Use a calculator to find each trigonometric ratio. Round to the nearest hundredth. a. tan 175° tan 175°  –0.09 b. cos 92°c. sin 160° cos 92°  –0.03sin 160°  0.34

5. Holt Geometry 8-5 Law of Sines and Law of Cosines You can use the altitude of a triangle to find a relationship between the triangle’s side lengths. In ∆ABC, let h represent the length of the altitude from C to From the diagram,, and By solving for h, you find that h = b sin A and h = a sin B. So b sin A = a sin B, and. You can use another altitude to show that these ratios equal

6. Holt Geometry 8-5 Law of Sines and Law of Cosines You can use the Law of Sines to solve a triangle if you are given two angle measures and any side length (ASA or AAS) or two side lengths and a non-included angle measure (SSA).

7. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree.

8. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree.

9. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree.

10. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree.

11. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree.

12. Holt Geometry 8-5 Law of Sines and Law of Cosines You can use the Law of Cosines to solve a triangle if you are given two side lengths and the included angle measure (SAS) or three side lengths (SSS).

13. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. XZ

14. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mTmT

15. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. DE

16. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mKmK

17. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. YZ

18. Holt Geometry 8-5 Law of Sines and Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mRmR

19. Holt Geometry 8-5 Law of Sines and Law of Cosines Use a calculator to find each trigonometric ratio. Round to the nearest hundredth. 1. tan 154° 2. cos 124° 3. sin 162°

20. Holt Geometry 8-5 Law of Sines and Law of Cosines Use ΔABC for Items 4–6. Round lengths to the nearest tenth and angle measures to the nearest degree. 4. mB = 20°, mC = 31° and b = 210. Find a. 5. a = 16, b = 10, and mC = 110°. Find c. 6. a = 20, b = 15, and c = 8.3. Find mA.

21. Holt Geometry 8-5 Law of Sines and Law of Cosines 7. An observer in tower A sees a fire 1554 ft away at an angle of depression of 28°. To the nearest foot, how far is the fire from an observer in tower B? To the nearest degree, what is the angle of depression to the fire from tower B?

22. Holt Geometry 8-5 Law of Sines and Law of Cosines Home Work PG# 555 18-36 evens, 40,42,46,48,50,51, 52,53