1. 1 What you will learn  How to solve triangles by using the Law of Sines if the measures of two angles and a side are given  How to find the area of a triangle if the measures of two sides and the included angle or the measures of two angles and a side are given

2. Objective: 5-6 Law of Sines 2 Introduction Over the next three sections, we are going to learn to solve triangles that are not right triangles. - Law of Sines (including a “special” case) - Law of Cosines

3. Objective: 5-6 Law of Sines 3 A Little Background A B D C How do you know? Therefore, angle D and angle C will have the same sine 2r

4. Objective: 5-6 Law of Sines 4 The Law of Sines The Law of Sines: Let triangle ABC be any triangle with a, b, and c representing the measures of the sides opposite the angles with measures A, B, and C respectively. What we are learning today applies to the following congruencies: ASA or AAS

5. Objective: 5-6 Law of Sines 5 Example  Solve triangle ABC if A = 33 o, B = 104 o and b = 37.9 A B C B=37.9

6. Objective: 5-6 Law of Sines 6 You Try  Solve triangle LMN if L = 29 o, M=112 o, and l=22. L M N

7. Objective: 5-6 Law of Sines 7 The Inevitable Word Problem  A baseball fan is sitting directly behind home plat in the last row of the upper deck of U.S. Cellular Field in Chicago. The angle of depression to home plate is 29 o 54’, and the angle of depression to the pitcher’s mound is 24 o 12’. In major league baseball, the distance between home plate and the pitcher’s mound is 60.5 feet. How far is the fan from home plate? Remember, the angle of elevation is congruent to the angle of depression (they are alternate interior angles). 60.5 ft. 24 o 12 d

8. Objective: 5-6 Law of Sines 8 Finding Area of Triangles When 2 Sides are Known Let triangle ABC be any triangle with a, b, and c representing the measures of the sides opposite the angles with measurements A, B, and C, respectively. Then the area, K, can be determined using one of the following formulas. K = ½ bc sin AK = ½ ac sin B K = ½ ab sin C

9. Objective: 5-6 Law of Sines 9 Example  Find the area of triangle ABC if a = 4.7, c = 12.4, and B = 47 o 20’ A B C 4.7 12.4 47 o 20’

10. Objective: 5-6 Law of Sines 10 You Try  Find the area of triangle ABC if b = 21.2, c = 16.5, and A = 25 o.

11. Objective: 5-6 Law of Sines 11 Area if Two Angles and One Side are Known Let triangle ABC be any triangle with a, b, and c representing the measures of the sides opposite the angles with measurements A, B, and C respectively. Then the area K can be determined using one of the following formulas.

12. Objective: 5-6 Law of Sines 12 Example Find the area of triangle DEF if d=13.9, D = 34.4 o, and E = 14.8 o D E F 13.9

13. Objective: 5-6 Law of Sines 13 You Try  Find the area of triangle JKL if j = 45.7, K = 111.1 o, and L = 27.3 o

14. Objective: 5-6 Law of Sines 14 Homework  page 316, 11, 13, 17-23 odd, 25, 28