1. Geometry IB Date: 4/22/2014 Question: How do we measure the immeasurable? SWBAT use the Law of Sines to solve triangles and problems Agenda Bell Ringer: Put up Assigned problems Go over 8.2/8.3 Quiz HW Requests – ws Angle of Elevation and Depression 8.5 pg 577 #8-11, 17-21, 23, 24, 38 HW: WS old textbook on Law of Sines Announcements:

2.  In trigonometry, we can use the Law of Sines to find missing parts of triangles that are not right triangles.  Law of Sines: In  ABC, sin A = sin B = sin C a b c B A C c b a

3. L.T.: Be able to use the Law of Sines to find unknowns in triangles! Quick Review: What does Soh-Cah-Toa stand for? What kind of triangles do we use this for? What if it’s not a right triangle? GASP!! What do we do then?? right triangles

4. Note:  capital letters always stand for __________!  lower-case letters always stand for ________! Use the Law of Sines ONLY when:  you DON’T have a right triangle AND  you know an angle and its opposite side A B C a b c sides angles

5. You are given a triangle, ABC, with angle A = 70°, angle B = 80° and side a = 12 cm. Find the measures of angle C and sides b and c. * In this section, angles are named with capital letters and the side opposite an angle is named with the same lower case letter.*

6. AC B 70° 80° a = 12 c b The angles in a ∆ total 180°, so angle C = 30°. Set up the Law of Sines to find side b:

7. Set up the Law of Sines to find side c: AC B 70° 80° a = 12 c b = 12.6 30°

8. Angle C = 30° Side b = 12.6 cm Side c = 6.4 cm AC B 70° 80° a = 12 c = 6.4 b = 12.6 30° Note: We used the given values of A and a in both calculations. Your answer is more accurate if you do not used rounded values in calculations.

9. Find p. Round to the nearest tenth.

10. Law of Sines Use a calculator. Divide each side by sin Cross products Answer:

11. Law of Sines Cross products Divide each side by 7. to the nearest degree in,

12. Solve for L. Use a calculator. Answer:

13. a. Find c. b. Find m  T to the nearest degree in  RST if r = 12, t = 7, and m  T = 76. Answer:

14.  The Law of Sines can be used to “ solve a triangle,” which means to find the measures of all of the angles and all of the sides of a triangle.

15. We know the measures of two angles of the triangle. Use the Angle Sum Theorem to find. Round angle measures to the nearest degree and side measures to the nearest tenth.

16. Angle Sum Theorem Subtract 120 from each side. Add. Since we know and f, use proportions involving

17. To find d: Law of Sines Cross products Substitute. Use a calculator. Divide each side by sin 8°.

18. To find e: Law of Sines Cross products Substitute. Use a calculator. Divide each side by sin 8°. Answer:

19. We know the measure of two sides and an angle opposite one of the sides. Law of Sines Cross products Round angle measures to the nearest degree and side measures to the nearest tenth.

20. Solve for L. Angle Sum Theorem Use a calculator. Add. Substitute. Divide each side by 16. Subtract 116 from each side.

21. Cross products Use a calculator. Law of Sines Divide each side by sin Answer:

22. a. Solve Round angle measures to the nearest degree and side measures to the nearest tenth. b. Round angle measures to the nearest degree and side measures to the nearest tenth. Answer:

23. A 46-foot telephone pole tilted at an angle of from the vertical casts a shadow on the ground. Find the length of the shadow to the nearest foot when the angle of elevation to the sun is Draw a diagram Draw Then find the

24. Since you know the measures of two angles of the triangle, and the length of a side opposite one of the angles you can use the Law of Sines to find the length of the shadow.

25. Cross products Use a calculator. Law of Sines Answer: The length of the shadow is about 75.9 feet. Divide each side by sin

26. A 5-foot fishing pole is anchored to the edge of a dock. If the distance from the foot of the pole to the point where the fishing line meets the water is 45 feet, about how much fishing line that is cast out is above the surface of the water? Answer: About 42 feet of the fishing line that is cast out is above the surface of the water.