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6.4 Proving and Using the Sine Law

Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.4 Proving and Using the Sine Law. 6.4 Proving and Using the Sine Law. Goal for Today: Apply what we have learned about the Sine law to analyze and solve problems involving triangles. 6.4 Proving and Using the Sine Law.

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6.4 Proving and Using the Sine Law

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  1. Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.4 Proving and Using the Sine Law

  2. 6.4 Proving and Using the Sine Law Goal for Today: • Apply what we have learned about the Sine law to analyze and solve problems involving triangles

  3. 6.4 Proving and Using the Sine Law • Recall that the Sine Law is: (if finding a side*) *Flip the formula if finding an angle

  4. 6.4 Proving and Using the Sine Law • Recall that the Sine Law is:

  5. 6.4 Proving and Using the Sine Law • Recall also, that we can use the Sine Law to solve for an unknown angle or side if we are given: • 2 sides and one angle across from a known side, or • 2 angles and any side

  6. 6.4 Proving and Using the Sine Law • A chandelier is suspended from the ceiling by two chains. One chain is 46cm long and forms an ∠ of 60° with the ceiling. The other chain is 64 cm long. What angle does the longer chain make with the ceiling?

  7. 6.4 Proving and Using the Sine Law A B 60° ? 46cm 64cm C

  8. 6.4 Proving and Using the Sine Law

  9. 6.4 Proving and Using the Sine Law

  10. Humour Break

  11. 6.4 Proving and Using the Sine Law • Two tracking stations, 20km apart, measure the ∠’s of elevation of a rocket that was launched with a weather satellite. From station A, the angle of elevation is 41°; from station B, it is 75°, as shown. What is the altitude of the rocket to the nearest tenth of a kilometre?

  12. 6.4 Proving and Using the Sine Law

  13. 6.4 Proving and Using the Sine Law

  14. 6.4 Proving and Using the Sine Law R 41° A 20km B C

  15. 6.4 Proving and Using the Sine Law • Let’s first calculate the length of RB • *∠RBA=180°-75°=105° • *∠ARB=180°-105°-75°=34°

  16. 6.4 Proving and Using the Sine Law R 23.5km 41° 75° A 20km B C

  17. 6.4 Proving and Using the Sine Law • Let’s first calculate the length of RB • *∠RBA=180°-75°=105° • *∠ARB=180°-105°-75°=34°

  18. 6.4 Proving and Using the Sine Law • To solve this question, an easier way would be to find side AR and then use the SIN primary trig ratio using AR and angle A in order to find side RC

  19. Homework • p.555, #1-11

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