Law of Sines AAS or ASA Find p

Law of Sines (AAS or ASA) Find p. Round to the nearest tenth. We are given measures of two angles and a nonincluded side, so use the Law of Sines to write a proportion.

Law of Sines (AAS or ASA) Law of Sines Cross Products Property Divide each side by sin Use a calculator. Answer: p ≈ 4. 8

Find c to the nearest tenth. A. 4. 6 B. 29. 9 C. 7. 8 D. 8. 5 A. B. C. D. A B C D

Law of Sines (SSA) Find x. Round to the nearest degree.

Law of Sines (SSA) Law of Sines m B = 50, b = 10, a = 11 Cross Products Property Divide each side by 10. Use the inverse sine ratio. Use a calculator. Answer: x ≈ 57. 4

Find x. Round to the nearest degree. A. 39 B. 43 C. 46 D. 49 A. B. C. D. A B C D

Law of Cosines (SAS) Find x. Round to the nearest tenth. Use the Law of Cosines since the measures of two sides and the included angle are known.

Law of Cosines (SAS) Law of Cosines Simplify. Take the square root of each side. Use a calculator. Answer: x ≈ 18. 9

Find r if s = 15, t = 32, and m R = 40. Round to the nearest tenth. A. 25. 1 B. 44. 5 C. 22. 7 D. 21. 1 A. B. C. D. A B C D

Law of Cosines (SSS) Find m L. Round to the nearest degree. Law of Cosines Simplify.

Law of Cosines (SSS) Subtract 754 from each side. Divide each side by – 270. Solve for L. Use a calculator. Answer: m L ≈ 49

Find m P. Round to the nearest degree. A. 44° B. 51° C. 56° D. 69° A. B. C. D. A B C D

Indirect Measurement AIRCRAFT From the diagram of the plane shown, determine the approximate width of each wing. Round to the nearest tenth meter.

Indirect Measurement Use the Law of Sines to find KJ. Law of Sines Cross products

Indirect Measurement Divide each side by sin . Simplify. Answer: The width of each wing is about 16. 9 meters.

The rear side window of a station wagon has the shape shown in the figure. Find the perimeter of the window if the length of DB is 31 inches. Round to the nearest tenth. A. 93. 5 in. B. 103. 5 in. C. 96. 7 in. D. 88. 8 in. A. B. C. D. A B C D

Solve a Triangle Solve triangle PQR. Round to the nearest degree. Since the measures of three sides are given (SSS), use the Law of Cosines to find m P. p 2 Cosines = 82 = = 9, and q = 7 r 2 + q 2 – 2 pq cos P Law of 92 + 72 – 2(9)(7) cos P p = 8, r

Solve a Triangle 64 = 130 – 126 cos P Simplify. – 66 = – 126 cos P Subtract 130 from each side. Divide each side by – 126. Use the inverse cosine ratio. Use a calculator.

Solve a Triangle Use the Law of Sines to find m Q. Law of Sines m P ≈ 58, p = 8, q = 7. Multiply each side by 7. Use the inverse sine ratio. Use a calculator.

Solve a Triangle By the Triangle Angle Sum Theorem, m R ≈ 180 – (58 + 48) or 74. Answer: Therefore, m P ≈ 58; m Q ≈ 48 and m R ≈ 74.

Solve ΔRST. Round to the nearest degree. A. m R = 82, m S = 58, m T = 40 B. m R = 58, m S = 82, m T = 40 C. m R = 82, m S = 40, m T = 58 D. m R = 40, m S = 58, m T = 82 A. B. C. D. A B C D