1. Law of Sines and Cosines
Section 6.1 and 6.2
Law of Sines and Cosines

2. If ABC is a triangle with sides a, b, c, then… Use the law when AAS, ASA, or SSA is known.

3. Ex 1. (AAS) Let C = 102. 3°, B = 28. 7°, and b = 27. 4 feet
Ex 1. (AAS) Let C = 102.3°, B = 28.7°, and b = 27.4 feet. Find the remaining angle and sides.

4. Ex 2. (ASA) Let A = 30°, B = 45°, and c = 32 feet
Ex 2. (ASA) Let A = 30°, B = 45°, and c = 32 feet. Find the remaining angle and sides.

5. Ex 3. (SSA) Find the missing information of the triangle.
47°
12 m
23 m

6. Law of Cosine Formulas: Use the law when SAS or SSS is known.

7. Ex 4. Find the remaining side and angles.
10 m 60˚ 14m

8. Ex 5. Find the remaining side and angles.
8 ft 30˚ 12 ft

9. Ex 6. Find the missing angles.
43 cm 39 cm 51 cm

10. Find the length of the pole.
Ex 7. A pole tilts towards the sun at an 8° angle from the vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43°. How tall is the pole?
Sketch the scenario.
Find the length of the pole.

11. Find the height of the tree.
Ex 8. Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical. At a point 30 meters from the tree in the direction towards the wind, the angle of elevation to the top of the tree is 22.5°. Find the height of the tree.
Sketch the scenario.
Find the height of the tree.

12. Ex 9. A plane leaves JFK International Airport and travels due west at 570 mph. Another plane leaves 20 minutes later and travels 22˚ west of north at a rate of 585 mph. To the nearest 10 miles, how far apart are the planes 40 minutes after the second plane leaves?