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

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Presentation transcript:

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 Recall that the Sine Law is: (if finding a side*) *Flip the formula if finding an angle

6.4 Proving and Using the Sine Law Recall that the Sine Law is:

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

6.4 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?

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

6.4 Proving and Using the Sine Law

Humour Break

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?

6.4 Proving and Using the Sine Law

A C 41° 20kmB R

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°

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

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°

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

Homework p.555, #1-11