LESSON 125 Problem Solving with Trigonometry 1 About 285 mih about 15 2 m A

# Lesson 125 problem solving with trigonometry 1 about

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LESSON 12.5 • Problem Solving with Trigonometry 1. About 2.85 mi/h; about 15° 2. m A 50.64°, m B 59.70°, m C 69.66° 3. About 8.0 km from Tower 1, 5.1 km from Tower 2 4. About 853 miles 5. About 530 ft of fencing; about 11,656 ft 2 LESSON 13.1 • The Premises of Geometry 1. a. Given b. Distributive property c. Subtraction property d. Addition property e. Division property 2. False 3. False 4. True; transitive property of congruence and definition of congruence 5. LESSON 13.2 • Planning a Geometry Proof Proofs may vary. 1. Flowchart Proof ABP CDQ CA Postulate PAB QCD Third Angle Theorem APQ CQD CA Postulate Given AB CD Given AP CQ ABP CDQ CA Postulate APB CQD CA Postulate ABP CDQ ASA Postulate CPCTC AB CD AB CD Given AP CQ Given PB QD Given B P D A B A M 7. RS 22.5 cm, EB 20 cm 8. x 20 cm; y 7.2 cm 9. p 1 3 6 5.3 cm; q 8 3 2.6 cm LESSON 12.1 • Trigonometric Ratios 1. sin P p r 2. cos P q r 3. tan P p q 4. sin Q q r 5. sin T 0.800 6. cos T 0.600 7. tan T 1.333 8. sin R 0.600 9. x 12.27 10. x 29.75 11. x 18.28 12. m A 71° 13. m B 53° 14. m C 30° 15. sin 40° 2 w 8 ; w 18.0 cm 16. sin 28° 1 x 4 ; x 7.4 cm 17. cos 17° 7 y 3 ; y 76.3 cm 18. a 28° 19. t 47° 20. z 76° LESSON 12.2 • Problem Solving with Right Triangles 1. Area 2 cm 2 2. Area 325 ft 2 3. Area 109 in 2 4. x 54.0° 5. y 31.3° 6. a 7.6 in. 7. Diameter 20.5 cm 8. 45.2° 9. 28.3° 10. About 2.0 m 11. About 445.2 ft 12. About 22.6 ft LESSON 12.3 • The Law of Sines 1. Area 46 cm 2 2. Area 24 m 2 3. Area 45 ft 2 4. m 14 cm 5. p 17 cm 6. q 13 cm 7. m B 66°, m C 33° 8. m P 37°, m Q 95° 9. m K 81°, m M 21° 10. Second line: about 153 ft, between tethers: about 135 ft LESSON 12.4 • The Law of Cosines 1. t 13 cm 2. b 67 cm 3. w 34 cm 4. m A 76°, m B 45°, m C 59° 5. m A 77°, m P 66°, m S 37° 6. m S 46°, m U 85°, m V 49° Discovering Geometry Practice Your Skills ANSWERS 113 ©2008 Key Curriculum Press
2. Proof: Statement Reason 1. CD BD 1. Given 2. BD AB 2. Given 3. CD AC 3. Given 4. AD is bisector 4. Converse of Angle of CAB Bisector Theorem 5. CAD BAD 5. Definition of angle bisector 6. ACD is a right 6. Definition of angle perpendicular 7. ABD is a right 7. Definition of angle perpendicular 8. ACD ABD 8. Right Angles Are Congruent Theorem 9. ABD ACD 9. SAA Theorem 3. Flowchart Proof 4. Proof: Statement Reason 1. AB BC 1. Given 2. ABC is isosceles 2. Definition of isosceles triangle 3. A ACB 3. IT Theorem 4. ACB DCE 4. Given NMO NOP IT Theorem QMN RON Supplements of Congruent Angles Theorem MNO is isosceles Definition of isosceles triangle Linear Pair Postulate QMN and NMO are supplementary Linear Pair Postulate RON and NOP are supplementary Transitivity MN NO Given MN QM Given NO QM 2. Flowchart Proof 3. Flowchart Proof LESSON 13.3 • Triangle Proofs Proofs may vary. 1. Flowchart Proof WXY WZY SAS Theorem XYM ZYM Definition of angle bisector XZY is isosceles Definition of isosceles triangle YM is angle bisector of XYZ Isosceles Triangle Vertex Angle Theorem Reflexive property WY WY Given XZ WY Given XY ZY YM is the altitude from vertex Y Definition of altitude and vertex angle a b c 180 ° Triangle Sum Theorem x b c 180 ° Substitution x y c 180 ° Substitution x y z 180 ° Substitution a x VA Theorem b y VA Theorem c z VA Theorem ABC Given PQR TSU AIA Theorem Converse of